Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Dang, Dinh H

Committee Member

Razzaghi, Mohsen

Committee Member

Smith, Robert C

Committee Member

Chuanxi, Qian

Committee Member

Woody, Jonathan R

Date of Degree

8-7-2020

Original embargo terms

Worldwide

Document Type

Dissertation - Open Access

Major

Mathematics

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

In this dissertation, we study the existence and nonexistence of positive solutions to some classes of singular p-Laplacian boundary value problems with a parameter. In the first study, we discuss positive solutions for a class of sublinear Dirichlet p- Laplacian equations and systems with sign-changing coefficients on a bounded domain of Rn via Schauder Fixed Point Theorem and the method of sub- and supersolutions. Under certain conditions, we show the existence of positive solutions when the parameter is large and nonexistence when the parameter is small. In the second study, we discuss positive radial solutions for a class of superlinear p- Laplacian problems with nonlinear boundary conditions on an exterior domain via degree theory and fixed point approach. Under certain conditions, we show the existence of positive solutions when the paprameter is small and nonexistence when the paramter is large. Our results provide extensions of corresponding ones in the literature from the Laplacian to the p-Laplacian, and can be applied to the challenging infinite semipositone case

URI

https://hdl.handle.net/11668/18012

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