Thesis & Dissertations

Existence of Solutions for non-homogeneous Anisotropic Eigenvalue Problems


Throughout this thesis, we will be studying the anisotropic eigenvalue problems using Orlicz-Sobolev spaces. The study will first consider the anisotropic nonlinear eigenvalue problem with variable exponent, which involves the ~p(:)-Laplace operator. One of the basic features of this study is that the differential operator involves partial derivatives with different variable exponents, therefore the framework will depend on anisotropic Sobolev and Lebesgue spaces. Secondly, more generic eigenvalue problem will be considered, which involves non-homogeneous operator on the divergence form, and since the problem of an anisotropic type, so the classical Orlicz-Sobolev space is inappropriate. This instructs us to study the problem in a more general Orlicz-Sobolev space, which will be presented later through this thesis. Finally,weareconsideringtwonewproblemsinvolvinglogarithmicoperatorsrelatedtoanisotro-pic eigenvalue problem.Eventually, the existence of new results will be determined.


Alaa Mohammad Al Sayyed


Housam Shrayteh, Toufic Mohamed Anis El- Arwadi