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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 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:
35J60Nonlinear elliptic equations
35B38Critical points in solutions of PDE
35J20Second order elliptic equations, variational methods
35D30Weak solutions of PDE
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