Multiple Sign Changing Solutions For Some Nonlinear Elliptic Partial Differential Equations In R～N

In our paper, we are interested in the existence and multiplicity of sign-changing solutions for some nonlinear elliptic partial differential equations in R^N.In the second chapter, we give some preliminaries. In the third chapter, we consider the existence and multiplicity of sign-changing solutions for the following p-Laplacian problem :where Under the suitable assumptions of f(x, u), combining the Principle of Symmetric Criticality, invariant set method and minimax method, we obtain an unbounded sequence of radial sign-changing solutions of (P₁). As N = 4 or N > 6, using Symmetric Mountain Pass Theorem and the Principle of Symmetric Criticality, we obtain an unbounded sequence of nonradal sign-changing solutions of (P₁).The forth chapter are devoted to study the existence and multiplicity of the nonlinear time-independent autonomous Schrodinger equations:where We assume f and a satisfy some suitable conditions. Combining the invariant set method and minimax method, we prove that there exists ∧ > 0 such that problem (P₂) has an unbounded sequence of radial sign-changing solutions, as λ > ∧. As N = 4 or N ≥ 6, using Fountain Theorem and the Principle of Symmetric Criticality, we obtain for given λ > 0, problem (P₂) has an unbounded sequence of nonradal sign-changing solutions.