A class of nonlinear Neumann problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions.

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

In this paper, we find two different solutions for the self-dual Maxwell–Higgs model coupled with gravitational fields by employing variational methods. One is a local minimizer and other mountain pass solution.

Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications partial differential equations involved mathematical physics. Starting from a variant of MPT, new concerning the existence solution for certain physics problems involving p-Laplacian and p-pseudo-Laplacian has been obtained. Based on main theorem, existence, possibly uniqueness, characterization...

The Sulphide Queen carbonatite deposit at Mountain Pass in southeast California is a world class rare earth element (REE) resource. This study images electrical resistivity structure of the REE and surrounding area to characterize resources under cover. An east-west elongated grid (35 × 15 km) 65 wideband magnetotelluric stations spanning from eastern Shadow Valley Ivanpah were collected modele...

In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtai...