EIGENVALUES OF SOME p(x)-BIHARMONIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS

In this paper, we study the following p(x)-biharmonic problem in Sobolev spaces with variable exponents {Delta(2)(p(x)) u = lambda (partial derivative F(x,u)/partial derivative u) x is an element of ohm, partial derivative u/partial derivative n = 0 x is an element of partial derivative ohm, partial derivative(|Delta u|(p(x)-2)Delta u)/partial derivative n = a(x)|u|(p(x)-2)u x is an element of partial derivative ohm. By means of the variational approach and Ekeland's principle, we establish that the above problem admits a nontrivial weak solution under appropriate conditions.