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Existence of three solutions for a non-homogeneous Neumann problem through Orlicz-Sobolev spaces. (English) Zbl 1220.35043
Summary: The aim of this paper is to establish a multiplicity result for an eigenvalue non-homogeneous Neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition. Precisely, a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate Orlicz-Sobolev space.
MSC:
35J60Nonlinear elliptic equations
58E05Abstract critical point theory
35D30Weak solutions of PDE
35J70Degenerate elliptic equations
46N20Applications of functional analysis to differential and integral equations
58J05Elliptic equations on manifolds, general theory
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