L(P)-SOLVABILITY OF A 4TH-ORDER BOUNDARY-VALUE PROBLEM AT RESONANCE

Let Omega be a bounded domain in R(n) with smooth boundary Gamma. We o btain existence results for the solutions of the biharmonic boundary v alue problems, -Delta(2)u + lambda(1)(2)u + g(x, u) = f, in Omega, u = Delta u = 0 on Gamma; -Delta(2)u + g(x,u) = f, in Omega, partial deri vative u/partial derivative n = partial derivative(Delta u)/partial de rivative n = 0, on Gamma when g(x, u) has linear growth in u and f is in certain subclass of L(p)(Omega). In the first problem, lambda(1) is the first eigenvalue of the eigenvalue problem -Delta u = lambda u in Omega and u = 0 on Gamma.