‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.

In this paper using the critical point theory of Chang [4] for locally Lipschitz functionals we prove an existence theorem for noncoercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.

This paper aims to show the existence of nontrivial solutions for discrete elliptic boundary value problems by using the “Mountain Pass Theorem”. Some conditions are obtained for discrete elliptic boundary value problems to have at least two nontrivial solutions. The results obtained improve the consequences of the known literature [Guang Zhang, Existence of nontrivial solutions for discrete el...

In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)−Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration–compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain...

By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltonian system ∆u(t− 2) +∇F (t, u(t)) = 0, for all t ∈ Z.

This work is devoted to study the existence of solutions to equations of the p-Laplacian type in unbounded domains. We prove the existence of at least one solution, and under further assumptions, the existence of in nitely many solutions. We apply the mountain pass theorem in weighted Sobolev spaces.