EXISTENCE RESULTS FOR A CLASS OF NON-UNIFORMLY ELLIPTIC EQUATIONS

We present existence results for a class of non-uniformly elliptic problems whose prototype is {-div(del u/(a(x) + u)alpha) = u(s) + f u(x) >= 0 u(x) = 0 where Omega is an open bounded subset of R-N, N >= 3, a(x) is a measurable function belonging to L-infinity(Omega) such that 0 < a(1) <= a(x) <= (a)2, for a. e. x is an element of Omega with a(1) and a(2) positive constants. Moreover we assume that alpha and s are real numbers such that 0 <= alpha < 1 and 0 <= s < 1 - alpha. Finally we assume that the datum f belongs to Lebesgue spaces L-m(Omega) where m varies in suitable intervals. We further present an existence result for nontrivial solutions to problem (0.1) when f equivalent to 0.