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Existence of three solutions for impulsive multi-point boundary value problems

Bohner M., Heidarkhani S., Salari A., Caristi G.

Opuscula Mathematica

2017

Vol. 37, no. 3

353--379

This paper is devoted to the study of the existence of at least three classical solutions for a second-order multi-point boundary value problem with impulsive effects. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. Also by presenting an example, we ensure the applicability of our results.

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.