THREE SOLUTIONS FOR A CLASS OF GRADIENT MIXED BOUNDARY VALUE SYSTEMS DEPENDING ON TWO PARAMETERS

In this paper we discuss the existence of at least three solutions for a class of gradient mixed boundary value systems. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited,Nonlinear Anal., 70:9(2009),3084-3089].     

Three solutions for an obstacle problem for a class of variational–hemivariational inequalities

In this paper, we consider a class of obstacle problems for variational–hemivariational inequalities, by using nonsmooth version of three points critical theory in [S.A. Marano, D. Motreanu, On a three critical points theorem for non-differentiable functions and application to nonlinear boundary value problems, Nonlinear Anal. 48 (2002) 37–52], the existence of three solutions for the problem is obtained.     

An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities

A multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.     

Existence of three solutions for a Neumann problem involving the p(x)‐Laplace operator

In this paper, we study the existence of three solutions to a Neumann problem with nonstandard growth conditions. The technical approach is mainly based on three critical points theorem due to Ricceri. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiple periodic solutions for non-linear difference systems involving the p-Laplacian

Using the three critical points theorem, Clark's theorem and the Morse theory, multiple periodic solutions for non-linear difference systems involving the p-Laplacian are obtained by variational methods.     

Some remarks on a three critical points theorem

Some remarks on a strict minimax inequality, which plays a fundamental role in Ricceri's three critical points theorem, are presented. As a consequence, some recent applications of Ricceri's theorem to nonlinear boundary value problems are revisited by obtaining more precise conclusions.     

具Neumann边界条件的拟线性椭圆方程组的多解存在性

通过运用Ricceri的一个三临界点定理，得到了一类具变分结构的拟线性椭圆方程组的多解的存在性．     

Three weak solutions for elliptic Dirichlet problems

An existence result of three non-zero solutions for non-autonomous elliptic Dirichlet problems, under suitable assumptions on the nonlinear term, is presented. The approach is based on a recent three critical points theorem for differentiable functionals.     

Three solutions for a class of quasilinear elliptic equation involving the p − q‐Laplace operator

The existence of at least three weak solutions is established for a class of quasilinear elliptic equation involving the p ? q‐Laplace operator with Dirichlet boundary condition. The technical approach is mainly on the basis of a three critical points theorem due to Ricceri. Copyright © 2013 John Wiley & Sons, Ltd.     

On a class of nonlinear variational–hemivariational inequalities

A three critical points theorem for nondifferentiable functions is pointed out and an existence result of multiple solutions for a Neumann elliptic variational–hemivariational inequality involving the p-laplacian is established. As an application, a Neumann problem for elliptic equations with discontinuous nonlinearities is studied.     

Multiplicity result for a discrete eigenvalue problem with discontinuous nonlinearities

Using a three critical points theorem for nondifferentiable functionals, we investigate a class of second order difference equation with discontinuous nonlinearities. A new multiplicity result is obtained.     

Existence of two local minima for functionals on reflexive Banach spaces

In this paper, we establish an existence theorem of two local minima for functionals on reflexive Banach space. As a consequence, we obtain an existence theorem of three critical points which improves the conclusion of a result in a recent paper of G.Bonanno concerning some remarks on a three-critical-points theorem established by B. Ricceri.     

Three solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. Multiplicity of solutions is obtained by three critical points theorem. An example is presented to illustrate main result.     

一个分歧定理

本文用 Morse 理论给出 Krasnoselski Rabinowitz 关于位算子分歧点定理的一个新的证明.设 H 是一个 Hilbert 空间,Ω 是 H 中零元θ的一个邻域.又设 L 是 H 上的一个有界自伴算子,而 G∈C(Ω,H)满足 G(u)=o(‖u‖),当 u→θ.倘若 G 还是一个位算子,即存在 g∈C~1(Ω,R~1),使得 dg=G.求解带参数 λ∈R~1的方程     

A boundary value problem associated to non-homogeneous operators in Orlicz-Sobolev spaces

We apply a three critical points theorem of B. Ricceri to establish the existence of at least three weak solutions for a class of non-homogeneous Neumann problems. Furthermore, by using another theorem of him, we prove that an appropriate oscillating behaviour of the nonlinear term ensures the existence of infinitely many weak solutions. Our analysis is based on recent variational methods for smooth functionals defined on Orlicz-Sobolev spaces.     

Multiplicity results of p(x)-Laplacian systems with Neumann conditions

In this paper, we study a Neumann problem for elliptic systems with variable exponents. We obtain the existence of at least three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem (Ricceri in Nonlinear Anal TMA 70:3084–3089, 2009).     

On a three critical points theorem

In this paper, using a recent result by J. Saint Raymond ([6]), we improve the three critical points theorem established in [5].     

Three critical points theorem and its application to quasilinear elliptic equations

In this paper, we prove a Pucci-Serrin type three critical points theorem for continuous functionals and study its application to quasilinear elliptic equations with natural growth.     

Three Solutions for a Partial Differential Inclusion Via Nonsmooth Critical Point Theory

The existence of three solutions for a partial differential inclusion involving a perturbed nonlinearity and two real parameters is proved. Moreover, an estimate of the norms of solutions, independent of both the parameters and the perturbation, is achieved. The main theoretical tool is an extension to nonsmooth functionals of a very recent three critical points theorem of Ricceri.     

一类具有p-Laplacian的非线性特征值问题

利用变分法中的一个三临界点定理,在适当的假设下,研究了一类具有p-Laplacian的特征值Dirichlet问题至少存在三个弱解的充分条件.