Infinitely many weak solutions for p(x)-Laplacian-like problems with sign-changing potential

摘要

This study is concerned with the p(x)-Laplacian-like problems and arising from capillarity phenomena of the following type ? ?? ?? ?div 1 + |?u| p(x) √ 1+|?u| 2p(x) |?u| p(x)?2?u = λ f(x, u), in ?, u = 0, on ??, where ? is a bounded domain in RN with smooth boundary ??, p ∈ C(?), and the primitive of the nonlinearity f of super-p + growth near infinity in u and is also allowed to be sign-changing. Based on a direct sum decomposition of a space W 1,p(x) 0 (?), we establish the existence of infinitely many solutions via variational methods for the above equation. Furthermore, our assumptions are suitable and different from those studied previously.