On the Existence of Infinitely Many Solutions of the Dirichlet Problem for Some Nonlinear Elliptic Equations

摘要

The existence of multiple solutions to nonlinear elliptic boundary value problems has been studied by many authors, especially when the nonlinear term is an odd function of the dependent variable. This paper shows, for a class of such equations, that when oddness is destroyed by adding a nonodd nonlinear perturbation to the equation, the resulting problem still possesses an infinite number of distinct solutions. (Author)