Opuscula Mathematica
Opuscula Math. 32, no. 3 (), 473-486
Opuscula Mathematica

On the existence of three solutions for quasilinear elliptic problem

Abstract. We consider a quasilinear elliptic problem of the type \(-\Delta_p u = \lambda (f(u)+\mu g(u))\) in \(\Omega\), \(u|_{\partial \Omega} =0\), where \(\Omega \in \mathbb{R}^N\) is an open and bounded set, \(f\), \(g\) are continuous real functions on \(\mathbb{R}\) and \(\lambda , \mu \in \mathbb{R}\). We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
Keywords: critical point, elliptic problem, minimax inequality, \(p\)-Laplacian, three critical points theorem, weak solution.
Mathematics Subject Classification: 35J20, 35J25, 35J92, 58E05.
Cite this article as:
Paweł Goncerz, On the existence of three solutions for quasilinear elliptic problem, Opuscula Math. 32, no. 3 (2012), 473-486, http://dx.doi.org/10.7494/OpMath.2012.32.3.473
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.