Multiple positive solutions for semipositone problems

TL;DRAbstract

"In this thesis we study the existence of solutions for a class of one dimensional, autonomous boundary value problems with Dirichlet boundary conditions. We shall first discuss certain types of multiplicity results starting with the existence of two or three solutions which occur surprisingly often for semipositone problems arising in diverse applications. We develop necessary and sufficient conditions for these cases as well as the conditions sufficient for an arbitrary number of solutions. Both the semipositone problem and the problem where f(0)=0 are considered. We also examine nonlinearities f with a variety of behaviors including superlinear, sublinear and bounded growth. In addition, we examine cases in which f has an arbitrary number of zero points. Finally we conclude with a discussion of how to construct example functions exhibiting the behaviors of the nonlinearities considered in this thesis."--Abstract from author supplied metadata

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