Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic \vec p-Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.

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Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Böhner

Caristi

Gharehgazlouei

et al. 2020

Nonautonomous Dynamical Systems

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Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

Abstract: Abstract. In this paper, we prove the existence of infinitely many solutions for the following system

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Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

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