MULTIPLICITY OF WEAK SOLUTIONS FOR A (P(X), Q(X))-KIRCHHOFF EQUATION WITH NEUMANN BOUNDARY CONDITIONS

The aim of this study is to investigate the existence of infinitely many weak solutions for the (p(x), q(x))-Kirchhoff Neumann problem described by the following equation : {- (a(1) + a(2) integral Omega 1/p(x) |del u|(p(x)) dx) Delta(p(center dot))u - (b(1) + b(2) integral(Omega) 1/q(x) |del u(|q(x)) dx) Delta(q(center dot))u +lambda(x)(|u|(p(x)-2)u + |u|(q(x)-2)u = f(1)(x, u) + f(2)(x, u) in Omega, partial derivative u/partial derivative nu = 0 on partial derivative Omega. By employing a critical point theorem proposed by B. Ricceri, which stems from a more comprehensive variational principle, we have successfully established the existence of infinitely many weak solutions for the aforementioned problem.