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Ground state solutions and multiple solutions for a p(x)-Laplacian equation in with periodic data

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In this work, we consider the following p(x)-Laplacian equation in where f, V and p(x) are periodic in . Under some appropriate assumptions, we prove the existence of the ground… Click to show full abstract

In this work, we consider the following p(x)-Laplacian equation in where f, V and p(x) are periodic in . Under some appropriate assumptions, we prove the existence of the ground state solutions via the generalized Nehari method due to Szulkin and Weth. Moreover, if f is odd in u, infinitely many pairs of geometrically distinct solutions are given. To the best of our knowledge, our results are new even in the constant exponent case.

Keywords: state solutions; ground state; equation periodic; laplacian equation

Journal Title: Complex Variables and Elliptic Equations
Year Published: 2017

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