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On the existence of three solutions for quasilinear elliptic problem

Goncerz P.

Opuscula Mathematica

2012

Vol. 32, no. 3

473-486

We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.

On minimax inequalities in topological spaces without convexity structure

Lu H.-S.

Journal of Applied Analysis

2007

Vol. 13, nr 1

133-149

In this paper, we give a new nonempty intersection theorem in general topological spaces without convexity structure. As its applications, some new minimax inequalities are obtained in general topological spaces without convexity structure.

A fixed point theorem for composed set-valued maps

Balaj M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

21-27

A fixed point theorem for the composition product of two set-valued maps is established. As an application of this result a generalization of Fan's minimax inequality is obtained.