Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations

The aim of this thesis is to prove the existence of a weak solution for semilinear fractional elliptic equations given by \begin{eqnarray*}\left\{ \begin{array}{ll} (-\Delta)^s u=|u|^{p-2} u+ f(x),& \quad x\in \Omega,\\ u=0, & \quad x \in \R^n \backslash \Omega, %0, & \quad x \in \partial \Oemga, \end{array} \right. \end{eqnarray*} where (-\Delta)^s denotes the fractional Laplace operator with $s \in (0,1],$ $n > 2s,$ $\Omega$ is an open bounded domain in \Rⁿ with C²-boundary and f \in L²(\Omega). We are interested in extending this result for $s \in (0, 1]$ to $p$ greater than the critical Sobolev exponent where the compact embedding fails to hold. We shall make use of a new variational principle presented in \cite{Mo1} that allows one to deal with problems well beyond the compact structure.

Name thesis:degree_name

Master of Science (M.Sc.)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Carleton University

Year dc:date.issued

2018

Author dc:creator

• Wong, Kok Lin

Statement dc:rights

• Copyright © 2018 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.

Language dc:language.iso

en

DOI

10.22215/etd/2018-13241

OAI identifier oai:identifier

oai:carleton.scholaris.ca:20.500.14718/38845