Degree Theory and Nonlinear Boundary Value Problems at Resonance

Consider the second order non-linear differential operator ${\cal L}y$ = Ly + $\eta y\sp3$, where $\eta$ = $\pm$1 and L, the linear part of ${\cal L}$, is of the form Ly = $y\sp{\prime\prime}$ + $p(x)y\sp\prime$ + q(x)y. Assume p(x) and q(x) are integrable on (a,b). We study the existence and uniqueness of solutions of ${\cal L}y$ = f satisfying linear boundary conditions on (a,b). The function f is an element of $L\sp1$ (a,b) Define BC = $\{y \in L\sp\infty$ (a,b): $y\sp\prime$ is absolutely continuous on (a,b), and y satisfies the boundary conditions$\}$. Assume the null space of L:BC $\to$ $L\sp1$ (a,b) is one-dimensional and spanned by $\varphi$. This is what is called the problem at resonance.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Lefton, Lew Edward

• Mathematics

Identifier

(UMI)AAI8721690

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71258