Partial Differential Equations with Variable Exponents —— Variational Methods and Qualitative Analysis

----- 偏微分方程变量指数：变分方法和定性分析

ISBN: 9781498703413 出版年：2015 页码：321 Radulescu, Vicentiu D Repovs, Dusan D CRC Press

Isotropic and Anisotropic Function Spaces Lebesgue and Sobolev Spaces with Variable Exponent History of function spaces with variable exponent Lebesgue spaces with variable exponent Sobolev spaces with variable exponent Dirichlet energies and Euler-Lagrange equations Lavrentiev phenomenon Anisotropic function spaces Orlicz spaces Variational Analysis of Problems with Variable Exponents Nonlinear Degenerate Problems in Non-Newtonian Fluids Physical motivation A boundary value problem with nonhomogeneous differential operator Nonlinear eigenvalue problems with two variable exponents A sublinear perturbation of the eigenvalue problem associated to the Laplace operator Variable exponents versus Morse theory and local linking The Caffarelli-Kohn-Nirenberg inequality with variable exponent Spectral Theory for Differential Operators with Variable Exponent Continuous spectrum for differential operators with two variable exponents A nonlinear eigenvalue problem with three variable exponents and lack of compactness Concentration phenomena: the case of several variable exponents and indefinite potential Anisotropic problems with lack of compactness and nonlinear boundary condition Nonlinear Problems in Orlicz-Sobolev Spaces Existence and multiplicity of solutions A continuous spectrum for nonhomogeneous operators Nonlinear eigenvalue problems with indefinite potential Multiple solutions in Orlicz-Sobolev spaces Neumann problems in Orlicz-Sobolev spaces Anisotropic Problems: Continuous and Discrete Anisotropic Problems Eigenvalue problems for anisotropic elliptic equations Combined effects in anisotropic elliptic equations Anisotropic problems with no-flux boundary condition Bifurcation for a singular problem modelling the equilibrium of anisotropic continuous media Difference Equations with Variable Exponent Eigenvalue problems associated to anisotropic difference operators Homoclinic solutions of difference equations with variable exponents Low-energy solutions for discrete anisotropic equations Appendix A: Ekeland Variational Principle Appendix B: Mountain Pass Theorem Bibliography Index A Glossary is included at the end of each chapter.