Multiple Positive Solutions Research Articles

Multiple positive solutions for Kirchhoff type problems with singularity and asymptotically linear nonlinearities

In this paper, we devote ourselves to investigating a nonlocal problem involving singularity and asymptotically linear nonlinearities. By using the variational and perturbation methods, we obtain the existence of two positive solutions which improve the existing result in the literature.

Fractional Hardy-Sobolev operator with sign-changing and singular nonlinearity

We study the following fractional equation with Hardy potential and singular nonlinearity where is a bounded domain in with smooth boundary , n>2s, , the sharp constant of the fractional Hardy Sobolev inequality, , with , such that , and is a sign-changing function such that . Using variational methods, we show existence, non-existence and multiplicity of positive solutions of with respect to the parameter λ.

Multiple positive solutions for a coupled system of nonlinear impulsive fractional differential equations with parameters

We consider the multiplicity of positive solutions (PSs) for a coupled system involving nonlinear impulsive fractional differential equations with parameters. By employing the classical Guo–Krasnosel’skii fixed point theorem, some sufficient criteria for the existence of multiple PSs in terms of different values of parameters are derived. As an application, an example is given to illustrate the theoretical results.

A Landesman–Lazer Local Condition for Semilinear Elliptic Problems

The objective of this paper is to study the existence, multiplicity and non existence of solutions for semilinear elliptic problems under a local Landesman–Lazer condition. There is no growth restriction at infinity on the nonlinear term and it may change sign. In order to establish the existence of solution we combine the Lyapunov–Schmidt reduction method with truncation and approximation arguments via bootstrap methods. In our applications we also consider the existence of a bifurcation point which may have multiple positive solutions for a fixed value of the parameters.

Standing waves for weakly coupled nonlinear Schrödinger systems

This paper is concerned with the application of variational methods in the study of positive solutions for a system of weakly coupled nonlinear Schrödinger equations in the Euclidian space. The results on multiplicity of positive solutions are established under the hypothesis that the coupling is either sublinear or superlinear with respect to one of the variables. Conditions for the existence or nonexistence of a positive least energy solution are also considered.

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form urn:x-wiley:mma:media:mma5519:mma5519-math-0001 where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.

Multiple positive solutions of a class of Schrödinger–Poisson equation involving indefinite nonlinearity in [formula omitted

In this paper, we study the existence of multiple positive solutions of Schrödinger–Poisson type equations with indefinite nonlinearity. Our main tool is the mountain pass theorem.

Existence results for Dirichlet problems about two mean curvature equations in Euclidean and Minkowski spaces

Let $$H_L$$ and $$H_R$$ be the extrinsic mean curvatures of a spacelike graph in Minkowski space $$\mathbb {L}^{N+1}$$ and Euclidean space $$\mathbb {R}^{N+1}$$ , respectively. In this paper, we establish the existence of multiple positive radial solutions for the Dirichlet problem of two nonlinear partial differential equations involving $$H_L$$ and $$H_R$$ .

Multiple positive solutions of second-order nonlinear difference equations with discrete singular φ-Laplacian

ABSTRACTWe consider the discrete boundary value problems with mean curvature operator in the Minkowski space where is a parameter, n>4 and q>1. Using upper and lower solutions, topological methods and Szulkin's critical point theory for convex, lower semicontinuous perturbations of -functionals, we show that there exists such that the above problem has zero, at least one or two positive solutions according to , or . Moreover, Λ is strictly decreasing with respect to n.

New multiple positive solutions for elliptic equations with singularity and critical growth

New multiple positive solutions for elliptic equations with singularity and critical growth

两点边值微分方程组多重正解的存在性

两点边值微分方程组多重正解的存在性

Multiple positive solutions of a boundary value problem of the fractional thermostat model

Multiple positive solutions of a boundary value problem of the fractional thermostat model

Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

Existence of multiple positive solutions for semipositone fractional boundary value problems

In this paper, we study the existence and multiplicity of positive solutions to the four-point boundary value problems of nonlinear semipositone fractional differential equations. Our results extend some recent works in the literature.

Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects

A nonlinear boundary value problem related to an equation of Kirchhoff type is considered. The existence of multiple positive solutions is proved through Avery-Peterson Fixed Point Theorem. A numerical method based on Levenberg-Marquadt algorithm combined with a heuristic process is present in order to align numerical and theoretical aspects.

Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects

A nonlinear boundary value problem related to an equation of Kirchhoff type is considered. The existence of multiple positive solutions is proved through Avery-Peterson Fixed Point Theorem. A numerical method based on Levenberg-Marquadt algorithm combined with a heuristic process is present in order to align numerical and theoretical aspects.

Multiplicity of Positive Solutions to the Boundary-Value Problems for Fractional Laplacians

For the problem (−Δ)su=uq−1 in the annulus ΩR = BR+1 \ BR ∈ ℝn, a so-called “multiplicity effect” is established: for each N ∈ ℕ there exists R0 such that for all R ≥ R0 this problem has at least N different positive solutions. (−Δ)s in this problem stands either for Navier-type or for Dirichlet-type fractional Laplacian. Similar results were proved earlier for the equations with the usual Laplace operator and with the p-Laplacian operator.

Global structure of positive solutions for problem with mean curvature operator on an annular domain

We study the global structure of positive solutions of the following mean curvature equation in the Minkowski space \[ -\div \bigg (\frac {\nabla u}{\sqrt {1-\vert \nabla u\vert ^2}}\bigg )= \lambda f(x,u), \] on an annular domain with the Robin boundary condition. According to the behavior of $f$ near $0$, we obtain the existence and multiplicity of positive solutions for this problem.

Multiple positive solutions for a class of (2, p)-Laplacian equation

In this work, we investigate the (2, p)-Laplacian equation −Δu − Δpu = f(x, u) in Ω with the boundary condition u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN, p > 2, and the nonlinearity f has extension property at both the zero and infinity points. We observe that the above equation admits at least two positive solutions, owing to the mountain pass theorem and Ekeland’s variational principle.

Multiplicity results for a boundary value problem with integral boundary conditions

The main purpose of this paper is to establish existence and multiplicity of positive solutions for a system of fourth-order boundary value problem with multi-point and integral conditions. To prove our results, we used Leggett–Williams fixed point theorem. An example is presented to illustrate our main results.