Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis (Hardcover)

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.