Sign changing solutions and multiple solutions of an elliptic eigenvalue problem with constraint in H 1 ( R N )
In this paper, we prove the existence of sign changing solutions and multiple solutions of a semilinear elliptic eigenvalue problem. One of the key points here is to construct nonempty invariant sets of the gradient flow which contain the positive and the negative solution of the problem.
sign changing solutions multiple solutions elliptic eigenvalue problem pseudo-gradient vector field