Multiple Positive Solutions for a Class of Nonlinear Elliptic Eigenvalue Problems with a Sign-Changing Nonlinearity

摘要

In 2009 Loc and Schmitt established a result on sufficient conditions formultiplicity of solutions of a class of nonlinear eignvalue problems for thep-Laplace operator under Dirichlet boundary conditions, extending an earlierresult of 1981 by Peter Hess for the Laplacian. Results on necessary conditionsfor existence were also established. In the present paper the authors extendthe main results by Loc and Schmitt to the $\Phi$-Laplacian. To overcome thedifficulties with this much more general operator it was necessary to employregularity results by Lieberman, a strong maximum principle by Pucci and Serrinand a general result on lower and upper solutions by Le.