On a resonant-superlinear elliptic problem

Cuesta, Mabel; de Figueiredo, Djairo G.; Srikanth, P.N.
July 2003
Calculus of Variations & Partial Differential Equations;Jul2003, Vol. 17 Issue 3, p221
Academic Journal
We start by discussing the solvability of the following superlinear problem ... where 1 < p < ... , O ? RN is a smooth bounded domain and f satisfies a one-sided Landesman-Lazer condition. We also consider systems of semilinear elliptic equations with nonlinearities of the above form, so exhibiting superlinearity as u ? + &infinity; and resonance as u ? -&infinity;. A priori bounds for the solutions of the equation and the system are obtained by using Hardy-type inequalities . Existence of solutions is then obtained using topological degree arguments.


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