无界域上带限制的非线性椭圆特征问题的多解和变号解

Multiple and Sign-changing Solutions for Nonlinear Elliptic Eigenvalue Problem with Constraint on Unbounded Domain

在径向对称的Sobolev空间中,利用约束变分方法,通过构造切伪梯度向量场,证明了无界区域上带限制的非线性椭圆特征问题正解、负解及变号解的存在性。

In this paper, we prove the existence of positive, negative and sign--changing solutions for a nonlinear elliptic eigenvalue problem with constraint on unbounded domain by using variational methods with constraint and by constructing tangent pseudogradient veetor field on radial symmetric Sobolev space.