Near Resonance Problems Of Semilinear Elliptic Equations And Systems

This dissertation investigates multiplicity of solutions for semilinear ellip-tic equations and systems near resonance at higher eigenvalues via variational methods and analysis techniques.Firstly, we study the semilinear elliptic equation whereΩ(?)RN is an open bounded domain with smooth boundary (?)Ω. We obtain two multiplicity results of solutions for above equation near resonance at higher eigenvalues when f satisfy sublincar conditions.Secondly, we consider the cooperative elliptic system whereΩ(?)RN is an open bounded domain with smooth boundary (?)Ω. We prove the multiplicity of solutions for above system near resonance at higher eigenvalues when▽For F satisfy some coercive conditions.And then, we study the degenerate equation whereΩ(?)RN is an open bounded domain with smooth boundary (?)Ω. Applying the compact imbedding H(?)(Ω.a)→LP(Ω) (p∈[1. (?))). we establish the multiplicity of solutions for this degenerate equation near resonance at higher eigenvalues.Lastly, we consider the semilincar elliptic equations with Hardy terms whereΩ(?)RN is an open bounded domain with smooth boundary (?)Ω. Like above degenerate equation, we prove the multiplicity results of solutions for this equation near resonance at higher eigenvalues.