ANISOTROPIC PROBLEMS WITH VARIABLE EXPONENTS AND CONSTANT DIRICHLET CONDITIONS

作者：Boureanu Maria Magdalena^*; Udrea Cristian; Udrea Diana Nicoleta

来源：Electronic Journal of Differential Equations, 2013, 220.

• Anisotropic variable exponent Sobolev spaces
• Dirichlet problem
• existence of weak solutions
• mountain pass theorem

We study a general class of anisotropic problems involving (p) over right arrow(.)-Laplace type operators. We search for weak solutions that are constant on the boundary by introducing a new subspace of the anisotropic Sobolev space with variable exponent and by proving that it is a reflexive Banach space. Our argumentation for the existence of weak solutions is mainly based on a variant of the mountain pass theorem of Ambrosetti and Rabinowitz.

• 出版日期2013-10-4