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Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces. (English) Zbl 1211.35117

Summary: We study a non-homogeneous boundary value problem in a smooth bounded domain in \(\mathbb R^N\). 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:

35J60 Nonlinear elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35J20 Variational methods for second-order elliptic equations
35D30 Weak solutions to PDEs
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