ONE SIDED RESONANCE FOR A MIXED BOUNDARY ELLIPTIC SYSTEM INVOLVING CRITICAL SOBOLEV EXPONENT

摘要

In this paper we study the existence of solutions for the system where Qf C RN is a bounded domain with smooth boundary a9 = rU u ,r and S are smooth (N - 1)-dimensional submanifolds of aQ with positivemeasures such that r n f = 0, v is the unit vector of the outward normalon 6a1, C1,C2 > 0, a,3 > 1 are real constants and a + / = 2*, where2* = 2N ,N > 3. Our main hypothesis is that the eigenvalues of thesymmetric matrix A = (b ca b) lies between two consecutive eigenvalues ofthe Laplacian operator under mixed boundary condition, allowing one sidedresonance for this system.