Order Periodic Boundary Value Problems Research Articles

Multiplicity of Solutions for Discrete 2n-TH Order Periodic Boundary Value Problem with φp-Laplacian

The purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions with the φp-Laplacian for the discrete 2n-th order periodic boundary value issue. To support these conclusions, we have employed variational techniques and contemporary critical point theory. A few new findings are expanded upon and enhanced. We give an example to show how our key findings can be applied.

Multiplicity of solutions for discrete 2n-th order periodic boundary value problem

Multiplicity of solutions for discrete 2n-th order periodic boundary value problem

USER-ORIENTED INTELLIGENCE MINING UNDER THE EXISTENCE OF SOLUTIONS TO INTEGRAL BOUNDARY VALUE PROBLEMS FOR FUZZY PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS

In order to accurately perceive user intention and improve the reliability of user intention information mining, the existence of solution of integral boundary value problem of fuzzy partial fractional differential equation is used to mine the information of user intention. Firstly, the periodic boundary value problem of fractional order fuzzy linear differential equation, periodic boundary value problem of fractional order fuzzy nonlinear differential equation and periodic boundary value problem of fractional order fuzzy coupled differential system are described in this research. The existence of the solution of the integral boundary value problem of the fuzzy partial fractional order differential equation is proved. Then a user-oriented information mining framework and an evaluation model based on the existence of solutions for the integral boundary value problem of fuzzy partial fractional differential equations are constructed. Finally, this research makes a case study and a comprehensive evaluation of user-oriented information mining based on the existence of solutions of integral boundary value problems for fuzzy partial fractional differential equations. The results show that the method based on the existence of the solution of the integral boundary value problem of fuzzy partial fractional order differential equation is feasible and scientific for the information mining of user intention. It is also concluded that this method is suitable for the modelling and solving of intelligence mining with complicated and unclear user intention. The research provides a good guidance for information mining oriented to user intention.

Nontrivial solutions for a second order periodic boundary value problem with the nonlinearity dependent on the derivative

In this paper, we study the existence of nontrivial solutions to the nonlinear differential equation with derivative term u′′(t)+a(t)u(t)=f(t,u(t),u′(t)),t∈[0,ω],u(0)=u(ω),u′(0)=u′(ω), where a: [0,ω]→R+(R+=[0,+∞)) is a continuous function with a(t)⁄≡0, and f: [0,ω]×R×R→R is continuous and may be sign-changing and unbounded from below. Without making any nonnegative assumption on the nonlinearity, by using the first eigenvalue corresponding to the relevant linear operator and the topological degree, the existence of nontrivial solutions to the above periodic boundary value problem is established in C1[0,ω] for the sublinear case. Moreover, two examples are given to demonstrate the validity of our main results.

Existence of nontrivial solutions for a nonlinear second order periodic boundary value problem with derivative term

In this paper, we study the existence of nontrivial solutions to the following nonlinear differential equation with derivative term: $$\begin{aligned} {\left\{ \begin{array}{l}u''(t)+a(t)u(t)=f\big (t,u(t),u'(t)\big ),\quad t\in [0,\omega ],\\ u(0)=u(\omega ),\quad u'(0)=u'(\omega ),\end{array}\right. } \end{aligned}$$ where a: $$[0,\omega ]\rightarrow \mathbb {R}^{+}\big (\mathbb {R}^{+}=[0,+\infty )\big )$$ is a continuous function with $$a(t)\not \equiv 0$$ , f: $$[0,\omega ]\times \mathbb {R}\times \mathbb {R}\rightarrow \mathbb {R}$$ is continuous and may be sign-changing and unbounded from below. Without making any nonnegative assumption on nonlinearity, using the first eigenvalue corresponding to the relevant linear operator and the topological degree, the existence of nontrivial solutions to the above periodic boundary value problem is established in $$C^1[0,\omega ]$$ . Finally, an example is given to demonstrate the validity of our main result.

Reversed <i>S</i> -shaped connected component for second-order periodic boundary value problem with sign-changing weight

In this paper, we consider the existence of an reversed S -shaped connected component in the set of positive solutions for second order periodic boundary value problem with a sign-changing weight function. By bifurcation technique, we identify the interval of bifurcation parameter in which the periodic boundary value problem has one or two or three positive solutions according to the asymptotic behavior of f at 0 and ∞.

Existence of Multiple Solutions to a Discrete Fourth Order Periodic Boundary Value Problem via Variational Method

By using variational methods and critical point theory, we obtain criteria for the existence of at least three solutions for a generalized fourth order nonlinear difference equation together with periodic boundary conditions. Various special cases of the above problem are discussed. An example is included to illustrate the results.

Existence of solutions to a discrete fourth order periodic boundary value problem

This paper is concerned with periodic boundary value problems for a fourth order nonlinear difference equation. Via variational methods and critical point theory, sufficient conditions are given for the existence of at least one solution, two solutions, and nonexistence of solutions. Our conditions do not involve the primitive function of the nonlinear term. Examples are provided to illustrate the applicability of the results.

Existence of positive solutions for a second order periodic boundary value problem with impulsive effects

In this paper, we are mainly concerned with the existence and multiplicity of positive solutions for the following second order periodic boundary value problem involving impulsive effects $$ \begin{cases} -u''+\rho^2u=f(t,u), & t\in J',\\ -\Delta u'|_{t=t_k}=I_k(u(t_k)), & k=1,\ldots,m,\\ u(0)-u(2\pi)=0,\quad u'(0)-u'(2\pi)=0. \end{cases} $$ Here $J'=J\setminus \{t_1,\ldots, t_m\}$, $f\in C(J\times \mathbb{R}^+, \mathbb{R}^+)$, $I_k\in C( \mathbb{R}^+, \mathbb{R}^+)$, where $ \mathbb{R}^+=[0,\infty)$, $J=[0,2\pi]$. The proof of our main results relies on the fixed point theorem on cones. The paper extends some previous results and reports some new results about impulsive differential equations.

MONOTONE GENERALIZED CONTRACTIONS IN ORDERED METRIC SPACES

In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and <TEX>$Rodr{\acute{i}}guez$</TEX>-<TEX>$L{\acute{o}}pez$</TEX> (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

Sharpening some core theorems of Nieto and Rodríguez-López with application to boundary value problem

AbstractIn this paper, we prove sharpened versions of some classical order-theoretic metrical fixed point theorems due to Nieto and Rodríguez-López (Order 22(3):223-239, 2005) using order-theoretic variants of completeness and continuity besides some another notions such as: the ICC property, the DCC property, and the MCC property. In this continuation, we further extend our results for Boyd-Wong type nonlinear contractions. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

Weak "Equation missing" -contractions on partially ordered metric spaces and applications to boundary value problems

Abstract A class of weak ψ -contractions satisfying the C -condition is defined on metric spaces. The existence and uniqueness of fixed points of such maps are discussed both on metric spaces and on partially ordered metric spaces. The results are applied to a first order periodic boundary value problem. MSC: 47H10, 54H25.

A second order periodic boundary value problem with a parameter and vanishing Green's functions

A second order periodic boundary value problem with a parameter and vanishing Green's functions

POSITIVE SOLUTION FOR A NONLINEAR FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM

The nonlinear fourth order periodic boundary value problem is studied.The existence of positive solution solution is proved under appropriate conditions by using the fixed point index and the property of Green's function.

Existence of Nontrivial Solutions for Second Order Impulsive Periodic Boundary Value Problems

In this paper,a class of second order periodic boundary value problem with impulsive effects is considered.The existence theorems of nontrivial solutions are obtained by virtue of variational methods and critical point theory.The results here extend the existing study.

The existence of solutions to nonlinear second order periodic boundary value problems

We consider the existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic solutions of some ϕ-Laplacian type equations and Duffing type equations are investigated.

Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral

We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.

Positive solutions of even order periodic boundary value problems

Positive solutions of even order periodic boundary value problems

Some existence results for a periodic problem with non-smooth potential

In this paper, two existence results for a class of second order periodic boundary value problems with non-smooth potential are obtained. We extend the Castro–Lazer–Thews reduction method to non-smooth functionals, the obtained result is then exploited to prove the existence of a nontrivial solution. Furthermore, we prove the existence of multiple solutions by using a multiplicity result based on local linking.

Bifurcation from interval and positive solutions for second order periodic boundary value problems

We give a global description of the branches of positive solutions of second order periodic boundary value problems u ″ - q ( t ) u + λ f ( t , u ) = 0 , 0 < t < 2 π , u ( 0 ) = u ( 2 π ) , u ′ ( 0 ) = u ′ ( 2 π ) , which are not necessarily linearizable. Our approach are based on topological degree and global bifurcation techniques.