We develop a min–max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable are asymptotic to the same cone and bound domain, there exists new self-expander trapped between two.

We study the existence of homoclinic solutions for semilinear p−Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis–Nirenberg’s Mountain Pass Theorem. Several examples and remarks are given.

Using Struwe’s “monotonicity trick” and the recent blow-up analysis of Ohtsuka and Suzuki, we prove the existence of mountain pass solutions to a mean field equation arising in two-dimensional turbulence.

Existence and multiplicity of weak solutions for an elliptic system is studied. By using Ekeland’s variational principle and the mountain pass theorem, we prove existence of at least three weak solutions. AMS Subject Classifications: 35J40, 35J67.

In this work we prove the existence of mountain pass solution for a fractional boundary value problem given by tD T (0D α t u(t)) = f(t, u(t)), t ∈ [0, T ] u(0) = u(T ) = 0.

The present paper deals with a nonlocal problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R . The problem studied is a stationary version of the original Kirchhoff equation involving the p-Laplace operator. The question of the existence of weak solutions is treated. Using variational approach and applying the Mountain Pass Theorem together with Fountai...

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 ...

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...

A. We consider the semi-linear elliptic PDEs driven by the fractional Laplacian: { (−∆)su = f (x, u), in Ω, u = 0, in Rn\Ω. By the Mountain Pass Theorem and some other nonlinear analysis methods, the existence and multiplicity of non-trivial solutions for the above equation are established. The validity of the Palais-Smale condition without AmbrosettiRabinowitz condition for non-local el...