This manuscript discusses the existence of nontrivial weak solution for following nonlinear eigenvalue problem driven by p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), x ? ?, u ?u 0, ??. Considering case 1 < min x?? p(x) max q(x) (N 2, Np(x) N 2p(x) ), we extend corresponding result reference [8], .p(x) 2 . The proofs main results are based on mount...

This work establishes the existence of positive solutions to a quasilinear singular elliptic equations involving (p-q)-Laplacian operator with singularities and vanishing potential. We adapt penalization method developed by del Pino Felmer we consider an auxiliary problem whose corresponding functional satisfies geometry mountain-pass theorem; then, prove that Palais-Smale sequences are bounded...

In this paper, we are concerned with some qualitative properties of the new fractional Musielak–Sobolev spaces WsLΦx,y such that generalized Poincaré type inequality and continuous compact embedding results. Moreover, prove any function in WsLΦx,y(Ω) may be extended to a WsLΦx,y(RN), Ω⊂RN is bounded domain class C0,1. addition, establish result relates complemented subspace WsLΦx,yRN. As an app...