Weak solution for fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition

Abstract

In the present paper, we prove the existence and uniqueness result of weak solutions to a class of fractional p(x)-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the varitional method combined with the theory of fractional Sobolev spaces with variable exponent. „«ï ®¤­®£® a« áã § ¤ ç ÷§ ¤à®¡®¢ ̈¬ p(x)-« ̄« á÷ ­®¬ § £à ­ ̈ç­®î 㬮¢®î â ̈ ̄㠄 ̈à ̈å«¥ ¤®¢¥¤¥­® ⥮६ã ̄à® ÷á­ã¢ ­­ï â õ¤ ̈­÷áâì á« ¡a®£® ஧¢'ï§aã. ‚ ̈a®à ̈á⮢ãîâìáï ¢ à÷ æ÷©­ ̈© ¬¥â®¤ ÷ ⥮à÷ï ¤à®¡®¢ ̈å ̄à®áâ®à÷¢ ‘®¡®«¥¢ §¬÷­­®£® ̄®àï¤aã.