ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES

We consider a boundary value problem of the form { -div(a(x)broken vertical bar del u broken vertical bar(P-2) is an element of- [g (x, u), g (x,u)] in Omega where Omega is a smooth bounded domain in R-N, p > 1, a is a weight function, and g x R 11 is a possibly discontinuous function. Using the BerkovitsTienari degree theory for upper semicontinuous set -valued operators of class (S+) in reflexive Banach spaces, we show that the corresponding integral operator equation can be solved in the weighted Sobolev spaces. Moreover, the solvability of the operator equation is discussed, depending on the least eigenvalue of the related eigenvalue problem.