Mississippi State University
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Dissertation - Campus Access Only
Doctor of Philosophy
James Worth Bagley College of Engineering
Department of Mathematics and Statistics
In this dissertation, we study the existence and multiplicity of positive solutions to classes of one-dimensional singular p-Laplacian problems with nonlinear and intergral boundary conditions when the reaction termis p-superlinear or p-sublinear at infinity. In the p-superlinear case, we prove the existence of a large positive solution when a parameter is small and if, in addition, the reaction term satisfies a concavity-like condition at the origin, the existence of two positive solutions for a certain range of the parameter. In the p-sublinear case, we establish the existence of a large positive solution when a parameter is large. We also investigate the number of positive solutions for the general PHI-Laplacian with nonlinear boundary conditions when the reaction term is positive. Our results can be applied to the challenging infinite semipositone case and complement or extend previous work in the literature.Our approach depends on Amann's fixed point in a Banach space, degree theory, and comparison principles.
Wang, Xiao, "Existence and multiplicity of positive solutions for one-dimensional p-Laplacian with nonlinear and intergral boundary conditions" (2021). Theses and Dissertations. 5290.