PERTURBED NONLINEAR ELLIPTIC NEUMANN PROBLEMS INVOLVING ANISOTROPIC SOBOLEV SPACES WITH VARIABLE EXPONENTS

In this paper we study the existence of infinitely many weak solutions of the following perturbed Kirchhoff-type non-homogeneous Neumann problem {-Sigma(N)(i=1) M-i (integral(Omega) 1/p(i)(x) vertical bar partial derivative u/partial derivative x(i)vertical bar(pi(x)) dx) partial derivative/partial derivative x(i) (vertical bar partial derivative u/partial derivative x(i)vertical bar(pi(x) 2) partial derivative u/partial derivative x(i)) + M-0 (integral(Omega) 1/p(0)(x) vertical bar u vertical bar(p0(x)-2) u = f(x,u) + g(x,u) in Omega, Sigma(N)(i=1) vertical bar partial derivative u/partial derivative x(i)vertical bar(pi(x)-2) partial derivative u/partial derivative x(i) v(i)=0 on partial derivative Omega, by applying technical approach based on critical points theorem due to B. Ricceri in a reflexive anisotropic Sobolev spaces. We use some suitable assumptions on the right had side but without using log-H older continu-ous condition.