EXISTENCE RESULTS FOR A CLASS OF NON-UNIFORMLY ELLIPTIC EQUATIONS OF p-LAPLACIAN TYPE.

In this paper, we establish the existence of non-trivial weak solutions in $W_0^{1,p} (\Omega)$, 1 < p < ∞, to a class of non-uniformly elliptic equations of the form \[ - {\rm div}({a({x,\nabla u})}) = \lambda f(u) + \mu g(u) \] in a bounded domain Ω of ℝN. Here a satisfies \[ |{a({x,\xi})}| \leqq c_0 ({h_0 (x) + h_1 (x)| \xi |^{p - 1}}) \] for all ξ ∈ ℝN, a.e. x ∈ Ω, $h_0 \in L^{\frac{p}{{p - 1}}} (\Omega)$, $h_1 \in L_{\rm loc}^1 (\Omega)$, h0(x) ≧ 0, h1(x) ≧ 1 for a.e. x in Ω. [ABSTRACT FROM AUTHOR]