Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Dang, Dinh H.

Committee Member

Qian, Chuanxi

Committee Member

Johnson, Corlis P.

Committee Member

Smith, Robert C.

Committee Member

Xu, Xiangsheng

Date of Degree

8-17-2013

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

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 radial solutions for classes of quasilinear elliptic equations and systems in a ball with Dirichlet boundary conditions. Our nonlinearities are asymptotically p-linear at infinity and are allowed to be singular at zero with non-positone structure, which have not been considered in the literature. In the one parameter single equation problem, we are able to show the existence of a positive radial solution with precise lower bound estimate for a certain range of the parameter. We also extend the study to a class of asymptotically p-linear system with two parameters and in the presence of singularities. We establish the existence of a positive solution with a precise lower bound estimate when the product of the parameters is in a certain range. Necessary and sufficient conditions for the existence of a positive solution are also obtained for both the single equation and system under additional assumptions. Our approach is based on the Schauder Fixed Point Theorem.

URI

https://hdl.handle.net/11668/21139

Comments

existence||radial solutions||p-Laplacian||nonexistence

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