Existence Of Positive Solutions Research Articles

Existence and Multiplicity of Positive Solutions for a Singular Third-Order Three-Point Boundary Value Problem with a Parameter

In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATION WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS

<abstract> In this paper, the existence of positive solutions for Caputo fractional differential equations boundary value problem with infinite points contained in the boundary value condition, and based on Green's function and its properties, the existence of multiple positive solutions are obtained by Avery-Peterson fixed point theorem. </abstract>

Bifurcationing Analysis of Predator-Prey Diffusive System Based on Bazykin Functional Response

A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.

Convergence conditions for continuous and discrete models of population dynamics

Some classes of continuous and discrete generalized Volterra models of population dynamics are considered. It is supposed that there are relationships of the type "symbiosis", "compensationism" or "neutralism" between any two species in a biological community. The objective of the work is to obtain conditions under which the investigated models possess the convergence property. This means that the studying system admits a bounded solution that is globally asimptotically stable. To determine the required conditions, the V. I. Zubov's approach and its discrete-time counterpart are used. Constructions of Lyapunov functions are proposed, and with the aid of these functions, the convergence problem for the considered models is reduced to the problem of the existence of positive solutions for some systems of linear algebraic inequalities. In the case where parameters of models are almost periodic functions, the fulfilment of the derived conditions implies that limiting bounded solutions are almost periodic, as well. An example is presented illustrating the obtained theoretical conclusions.

Positive solutions to three classes of non-local fourth-order problems with derivative-dependent nonlinearities

In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under the boundary conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound on the third-order derivative term, and the theory of fixed-point index is used on suitable open sets to obtain the existence of positive solutions. The nonlinearities have quadratic growth in the third-order derivative term. Previous results in the literature are not applicable in our case, as shown by our examples.

Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem

In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.

Positive solutions for a system of Hadamard fractional $ (\varrho_{1}, \varrho_{2}, \varrho_{3}) $-Laplacian operator with a parameter in the boundary

&lt;abstract&gt;&lt;p&gt;In this paper, we are gratified to explore existence of positive solutions for a tripled nonlinear Hadamard fractional differential system with $ (\varrho_{1}, \varrho_{2}, \varrho_{3}) $-Laplacian operator in terms of the parameter $ (\sigma_{1}, \sigma_{2}, \sigma_{3}) $ are obtained, by applying Avery-Henderson and Leggett-Williams fixed point theorems. As an application, an example is given to illustrate the effectiveness of the main result.&lt;/p&gt;&lt;/abstract&gt;

Existence of solutions for fractional differential equation with periodic boundary condition

&lt;abstract&gt;&lt;p&gt;We investigate the existence of solutions for a Caputo fractional differential equation with periodic boundary condition. Using the positivity of Green's function of the corresponding linear equation, we show the existence of positive solutions by using Krasnosel'skii fixed point theorem. Meanwhile, by using monotone iterative method and lower and upper solutions method, we also discuss the existence of extremal solutions for a special case.&lt;/p&gt;&lt;/abstract&gt;

Positive Solutions for a Class of Quasilinear Schr&amp;amp;#246;dinger Equations with Nonlocal Term

This paper is considered the existence of positive solutions for a class of generalized quasilinear Schrödinger equations with nonlocal term in RN which have appeared from plasma physics, as well as high-power ultrashort laser in matter. We use a charge of variables and obtain the existence of solutions via minimization argument.

Existence of positive solutions for a class of fractional Choquard equation in exterior domain

&lt;p style='text-indent:20px;'&gt;In this paper we show existence of positive solutions for a class of problems involving the fractional Laplacian in exterior domain and Choquard type nonlinearity. We prove the main results using variational method combined with Brouwer theory of degree and Deformation Lemma..&lt;/p&gt;

Positive solutions for second order impulsive differential equations with integral boundary conditions on an infinite interval

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main results.

A Sub‐Supersolution Method for p‐Laplacian Equation with Non‐Local Term

This paper is concerned with the existence of solutions for p‐Laplace problems with non‐local term. We prove the sub‐supersolution theorem using the pseudomonotone operator theorem and Minty–Browder theorem with appropriate assumptions on M, gi(i = 1,2). Then, using the sub‐supersolution approach, we determine the existence of positive solutions to specific problems.

Existence and simulation of positive solutions for m-point fractional differential equations with derivative terms

Abstract In this article, we investigate the existence of positive solutions for a class of m m -point fractional differential equations whose nonlinear terms involve derivatives. By using the properties of the Green function and fixed point theorems, some new conditions for the existence of at least one, two, three, and 2 n − 1 2n-1 positive solutions are established. As verification, some simulation examples are given to illustrate the main results. It is worth mentioning that we study the m m -point fractional differential equations with nonlinear terms involving derivative and use the iterative method to simulate our examples and give the approximate solution.

Positive solutions of a class of nonlinear boundary value fractional differential equations

In this paper, the existence of positive solutions of a class of nonlinear fractional boundary value problemsis considered. Two fixed point theorems are used, namely: Banach Contraction mapping principle andLeggett-Williams fixed point theorems. The former is used to prove the existence of a unique solution, whereasthe latter is used to prove the existence of at least three positive solutions to the problem. Some examples areprovided to illustrate the two results.

Positive solution of Hilfer fractional differential equations with integral boundary conditions

In this article, we have interested the study of the existence and uniqueness of positive solutions of the first-order nonlinear Hilfer fractional differential equation $$D_{0^{+}}^{\alpha ,\beta }y(t)=f(t,y(t)),\text{ }0&lt;t\leq 1,$$ with the integral boundary condition $$I_{0^{+}}^{1-\gamma }y(0)=\lambda \int_{0}^{1}y(s)ds+d,$$ where $0&lt;\alpha \leq 1,$ $0\leq \beta \leq 1,$ $\lambda \geq 0,$ $d\in \mathbb{R}^{+},$ and $D_{0^{+}}^{\alpha ,\beta }$, $I_{0^{+}}^{1-\gamma }$ are fractional ope\-rators in the Hilfer, Riemann-Liouville concepts, respectively. In this approach, we transform the given fractional differential equation into an equivalent integral equation. Then we establish sufficient conditions and employ the Schauder fixed point theorem and the method of upper and lower solutions to obtain the existence of a positive solution of a given problem. We also use the Banach contraction principle theorem to show the existence of a unique positive solution. The result of existence obtained by structure the upper and lower control functions of the nonlinear term is without any monotonous conditions. Finally, an example is presented to show the effectiveness of our main results.

Existence of positive solutions for a class of BVPs in Banach spaces

In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.

Coexistence states of a Lotka Volterra cooperative system with cross diffusion

In this work we study the steady state cross diffusive Lotka Volterra cooperative system. We have incorporated different type of cross diffusive term at each trophic level. Using bifurcation theory, we derive sufficient conditions which ensures existence of positive solutions of the system. The analysis carried out allows us to give an affirmative answer to the question that whether cooperative species under the influence of cross diffusion can co exist or not. We have also compared the results obtained for the competitive Lotka Volterra system with our results and an ecological explanation is provided to understand the difference. • To study a cooperative Lotka Volterra prey predator system with different type of cross diffusion at each trophic level. • To show using bifurcation theory that these positive solution branches tend to have an extension that is globally defined. • To find out through the analysis carried out whether a cross diffusive cooperative system admits coexistence states. • Comparison of the results with the corresponding predator prey system.

Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

Existence of positive solutions to nonlinear integral equations on the Heisenberg group

This paper is concerned with the existence and nonexistence of positive solutions for the nonlinear integral equations with weights related to the sharp Hardy–Littlewood–Sobolev (hereinafter referred to as HLS) inequality on bounded domains of the Heisenberg group : where q>1, , , Q = 2n + 2 is the homogeneous dimension of , , is a smooth bounded domain and is nonnegative continuous in .

On positive solutions of second-order delayed differential system with indefinite weight

In this paper, we study the existence of positive solutions of a second-order delayed differential system, in which the weight functions may change sign. To prove our main results, we apply Krasnosel’skii’s fixed point theorems in cones.