Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz–Sobolev spaces

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz–Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in 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 Lemm...

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Veröffentlicht in:Applied mathematics and computation 2011-03, Vol.217 (14), p.6624-6632
Hauptverfasser: MIHAILESCU, Mihai, REPOVS, Dušan
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
Calculus of variations and optimal control
Computation
Critical point
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematical models
Mathematics
Mountains
Non-homogeneous differential operator
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Orlicz–Sobolev space
Partial differential equations, boundary value problems
Sciences and techniques of general use
Variational methods
Weak solution
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Beschreibung
Zusammenfassung:We study a non-homogeneous boundary value problem in a smooth bounded domain in 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.050