Alexandru Kristály

A non-smooth three critical points theorem with applications in differential inclusions

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole

Set-valued versions of Ky Fan's inequality with application to variational inclusion theory

{\mathbb R^N}

Spectral estimates for a nonhomogeneous difference problem

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On the Schrödinger–Maxwell system involving sublinear terms

We consider the discrete boundary value problem (P): where the nonlinear term has an oscillatory behaviour near the origin or at infinity. By a direct variational method, we show that (P) has a sequence of non-negative, distinct solutions which converges to 0 (respectively ) in the sup-norm whenever f oscillates at the origin (respectively at infinity).

Location of Nash equilibria: A Riemannian geometrical approach

In this paper, we prove two set-valued versions of Ky Fans minimax inequality. From these results, versions of Schauders and Kakutanis fixed point theorems can be deduced. We formulate a variational inclusion problem for set-valued maps and a differential inclusion problem, concerning the contingent derivative. Sufficient conditions for the existence of solution for these inclusion problems are obtained, generalizing classical variational inequality problems.

What Do `Convexities' Imply on Hadamard Manifolds?

For certain positive numbers μ and A, we establish the multiplicity of solutions to the problem.

Nonsmooth Neumann-Type Problems Involving the p-Laplacian

We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

Singular Poisson equations on Finsler–Hadamard manifolds

Abstract In this paper, we study the coupled Schrodinger–Maxwell system ( S M λ ) { − Δ u + u + e ϕ u = λ α ( x ) f ( u ) in R 3 , − Δ ϕ = 4 π e u 2 in R 3 , where e > 0 , α ∈ L ∞ ( R 3 ) ∩ L 6 / ( 5 − q ) ( R 3 ) for some q ∈ ( 0 , 1 ) , and the continuous function f : R → R is superlinear at zero and sublinear at infinity, e.g., f ( s ) = min ( | s | r , | s | p ) with 0 r 1 p . First, for small values of λ > 0 , we prove a non-existence result for ( S M λ ) , while for λ > 0 large enough, a recent Ricceri-type result guarantees the existence of at least two non-trivial solutions for ( S M λ ) as well as the ‘stability’ of system ( S M λ ) with respect to an arbitrary subcritical perturbation of the Schrodinger equation.