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Three Solutions Theorem for a Quasilinear Dirichlet Boundary Value Problem

Goncerz P.

Schedae Informaticae

2012

Vol. 21

159--168

We consider a Dirichlet boundary value problem driven by the p-Laplacian with the right hand side being a Carathéodory function. The existence of solutions is obtained by the use of a special form of the three critical points theorem.

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.