CEU eTD Collection (2011); Mihailescu, Mihai Gheorghe: Eigenvalue Problems for Some Elliptic Partial Differential Operators

CEU Electronic Theses and Dissertations, 2011
Author Mihailescu, Mihai Gheorghe
Title Eigenvalue Problems for Some Elliptic Partial Differential Operators
Summary In this thesis we will study eigenvalue problems associated with some elliptic partial differential operators. In a very general framework the {\it model} equations that will be considered here have one of the forms
\begin {equation}\labe l{1Model1}
- {\rm div}(\phi(x,\nabla u))=\lambda f(x,u)
\end{equation} or
\begin{eq uation}\label{2 Model2}
-\su m\limits_{i=1}^ N\partial_{x_i} (\phi_i(x,\part ial_{x_i}u))=\l ambda f(x,u)\,,
\end{equation} where in the left-hand side we consider elliptic differential operators that can be linear or nonlinear, homogeneous or nonhomogeneous, while in the right-hand side $\lambda$ is a real number and $f$ is a given function. In this context, the concept of {\it eigenvalue} reads as follows: $\lambda$ is an {\it eigenvalue} of problem \eq{1Model1} (or \eq{2Model2}) if the problem possesses a non-trivial solution $u$ (here, solutions are understood in the sense of distributions).
Supervisor Morosanu, Gheorghe
Department Mathematics PhD
Full texthttps://www.etd.ceu.edu/2011/mihailescu_mihai.pdf

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