This paper studies the existence of multiple solutions of the second-order difference boundary value problem Δ2u n − 1 V ′ u n 0, n ∈ Z 1, T , u 0 0 u T 1 . By applying Morse theory, critical groups, and the mountain pass theorem, we prove that the previous equation has at least three nontrivial solutions when the problem is resonant at the eigenvalue λk k ≥ 2 of linear difference problem Δ2u n...

In this paper, we study a kind of anisotropic p-Laplacian equations in R n. Nontrivial solutions are obtained using mountain pass theorem given by Ambrosetti-Rabinowitz [1].

This paper is concerned with the existence of homoclinic solutions for a class of second order p-Laplacian systems with impulsive effects. A new result is obtained under more relaxed conditions by using the mountain pass theorem, a weak convergence argument, and a weak version of Lieb’s lemma. MSC: 34C37; 35A15; 37J45; 47J30

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.

Let Ω be a bounded subset of Rn with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

In this paper, we study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian systems ẍ(t) + V ′(t, x(t)) = 0, where t ∈ R, x ∈ R and V ∈ C(R × R ,R). By using a symmetric mountain pass theorem, we obtain a new criterion to guarantee that second-order Hamiltonian systems has infinitely many periodic solutions. We generalize and improve recent results fro...

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

By a variant version of mountain pass theorem, the existence and multiplicity of solutions are obtained for a class of superlinear p-Laplacian equations: −Δ p u = f (x,u). In this paper, we suppose neither f satisfies the superquadratic condition in Ambrosetti-Rabinowitz sense nor f (x,t)/|t| p−1 is nondecreasing with respect to |t|. This is an open access article distributed under the Creative...

Since A. Ambrosetti and P.H. Rabinowitz proposed the mountain pass theorem in 1973 (see [1]), critical point theory has become one of the main tools for finding solutions to elliptic problems of variational type. Especially, elliptic problem (1.2) has been intensively studied for many years. One of the very important hypotheses usually imposed on the nonlinearities is the following Ambrosetti-R...