‎in this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for szulkin-type functionals.

 ‎In this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎Our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for Szulkin-type functionals.

Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing. 1. Introduction. In this paper, using the critical-point theory of Szulkin ...

We propose a direct approach for detecting arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms. Although the method works in various frameworks, we illustrate it on the problem ⎪⎨ ⎪⎩ − u+ u=Q(x)[f (u)+ εg(u)], x ∈RN, N 2, u 0, u(x)→ 0 as |x| →∞, (Pε) where Q :RN →R is a radial, positive potential, f : [0,∞)→R is a continuous nonlinearity which oscillates near ...

We establish the existence of a nontrivial solution to systems of coupled Poisson equations with critical growth in unbounded domains. The proofs rely on a generalized linking theorem due to Krysewski and Szulkin [9], and on a concentration-compactness argument since the Palais-Smale condition fails at all critical levels. Mathematical Subject Classification. 35J50, 35J55

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

In this paper, we prove the existence and multiplicity of solutions for a large class quasilinear problems on nonreflexive Orlicz-Sobolev space. Here, use variational methods developed by Szulkin combined with some properties weak$^*$ topology.