Superlinear Elliptic Equations, Existence And Multiplicity

This dissertation investigates the existence and multiplicity of solutions for superlinear elliptic equations without(AR)condition via variational methods.Firstly,we consider the following elliptic equation with Dirichlet boundary value condition where△pu=div(|▽u|)is the p-Laplacian operator,p>1,Ωis a bounded domain in IRN(N≥1) with smooth boundary (?)Ω.f∈C(Ω×IR,IR)is superlinear at infinity related to t,that is, (F) lim (?)=＋∞uniformly for a.e. x∈Ω. We prove the existence and multiplicity of solutions for the above equation by a variant of mountain pass theorem under condition(F).And then we study a class of elliptic equation involving a parameter Whereλ>0 is a parametcr.p>1.Ωis a bounded domain in IR(N≥1)with smooth boundary (?)Ω.f∈C(Ω×IR,IR) and satisfies condition(F).For every入>0,we obtain a positive solut ion and a negative one.Lastly,we study a class of superlinear elliptic equations with a concave and convex nonlinearities where 1