Multiplicity Of Solutions For Nonlinear Elliptic Equations

This thesis mainly considers the multiplicity of solutions for elliptic equations and systems. It consists of three parts.In the first part, we consider equation Assume that a satisfies some compactness condition;f is a p-super linear and sub-critical nonlinear term; a and f are radially symmetric with respect to the first two coordinates. We prove that for any positive integer m, problem (Pλ) has a solution with at least2m nodal domains when λ is large enough.In the second part, we consider the existence and multiplicity of non-radially symmetric solutions for Schrodinger systems as follows, Assume that a and b satisfies some compactness condition and they are radially symmetric with respect to the first two coordinates and λ∈(0,1). We prove that for any positive integer l, problem (Sλ) has a nontrivial solution (ul,vl). Moreover both ul and vl have at least2l nodal domains.In the third part, we consider the following coupled elliptical systems: Assume that a and b satisfies some compactness conditions;f and g are superlinear and subcritical nonlinear terms and β (0,1). We obtain the existence of infinitely many solutions for(Sβ).