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 text | https://www.etd.ceu.edu/2011/mihailescu_mihai.pdf |
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