We discuss Neumann and Robin problems driven by the p-Laplacian with jumping nonlinearities. Using sub-sup solutionmethod, Fucı́k spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equ...

We provide a max-min characterization of the mountain pass energy level for a family of variational problems. As a consequence we deduce the mountain pass structure of solutions to suitable PDEs, whose existence follows from classical minimization argument. In the literature the existence of solutions for variational PDE is often reduced to the existence of critical points of functionals F havi...

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous p(x)- Laplacian equations, managed by non polynomial growth operator in framework variable exponent Sobolev spaces on Riemannian manifolds. mountain pass Theorem is used.

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [16]. Math Subject Classifications: 39A10, 34B18, 58E30.

The aim of this paper is to establish the existence at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

We consider the following nonlinear singular elliptic equation −div (|x| −2a ∇u) = K(x)|x| −bp |u| p−2 u + λg(x) in R N , where g belongs to an appropriate weighted Sobolev space, and p denotes the Caffarelli–Kohn– Nirenberg critical exponent associated to a, b, and N. Under some natural assumptions on the positive potential K(x) we establish the existence of some λ 0 > 0 such that the above pr...

Correspondence should be addressed to Yongkun Li, [email protected] Received 16 December 2010; Revised 6 February 2011; Accepted 11 February 2011 Academic Editor: Dumitru Motreanu Copyright q 2011 Y. Li and T. Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the...

This paper focuses on the following elliptic equation { − u ′′ − p(x)u = f(x,u), a.e. x ∈ [0, l], u(0) − u(l) = u ′(0) − u ′(l) = 0, where the primitive function of f(x,u) is either superquadratic or asymptotically quadratic as |u| → ∞, or subquadratic as |u| → 0. By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establi...

In this paper, we obtain a version of Ekeland's variational principle for interval-valued functions by means the Dancs-Hegedüs-Medvegyev theorem (Dancs et al. (1983) [14]). We also derive two versions involving generalized Hukuhara Gâteaux differentiability as well bifunctions. Finally, apply these new to fixed point theorems, optimization problems, Mountain Pass Theorem, noncooperative games, ...