We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.

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.

In this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least k connected components, then our problem has at least k periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument.

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke's theorems.

Using the Fenchel-Young duality and mountain pass geometry we derive a new multiple critical point theorem. In a finite dimensional setting it becomes three critical point theorem while in an infinite dimensional case we obtain the existence of at least two critical points. The applications to anisotropic problems show that one can obtain easily that all critical points are nontrivial.

Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in RN . These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superf...

We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with p-Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions. 2012 Elsevier Inc. All rights reserved.