Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Hai Dang
Committee Member
Chuanxi Qian
Committee Member
Mohsen Razzaghi
Committee Member
Mohammad Sepehrifar
Committee Member
Robert Smith
Date of Degree
8-6-2021
Original embargo terms
Visible to MSU only for 6 months
Document Type
Dissertation - Open Access
Major
Mathematics
Degree Name
Doctor of Philosophy
Degree Name
Doctor of Philosophy (Ph.D)
College
College of Arts and Sciences
College
College of Arts and Sciences
Department
Department of Mathematics and Statistics
Department
Department of Mathematics and Statistics
Abstract
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.
Recommended Citation
Wang, Xiao, "Existence and multiplicity of positive solutions for one-dimensional p-Laplacian with nonlinear and intergral boundary conditions" (2021). Theses and Dissertations. 5290.
https://scholarsjunction.msstate.edu/td/5290