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Zbl 1211.35117
Mihăilescu, Mihai; Repovš, Dušan
Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces. (English)
[J] Appl. Math. Comput. 217, No. 14, 6624-6632 (2011). ISSN 0096-3003

Summary: We study a non-homogeneous boundary value problem in a smooth bounded domain in $\Bbb R^N$. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.

MSC 2000:: *35J60 Nonlinear elliptic equations
35B38 Critical points
35J20 Second order elliptic equations, variational methods
35D30

Keywords: non-homogeneous differential operator; Orlicz-Sobolev space; critical point; weak solution

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