Vicentiu D. Radulescu

Partial differential equations with variable exponents : variational methods and qualitative analysis

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.

Combined effects in nonlinear problems arising in the study ofanisotropic continuous media

We are concerned with the Lane-Emden-Fowler equation −∆u = λk(x)u ± h(x)u in Ω, subject to the Dirichlet boundary condition u = 0 on ∂Ω, where Ω is a smooth bounded domain in R , k and h are variable potential functions, and 0 < q < 1 < p. Our analysis combines monotonicity methods with variational arguments.

Solutions with sign information for nonlinear nonhomogeneous elliptic equations

We consider a class of nonlinear, coercive elliptic equations driven by a nonhomogeneous differential operator. Using variational methods together with truncation and comparison techniques, we show that the problem has at least three nontrivial solutions, all with sign information. In the special case of

Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media

(p,2)

Existence results for variational-hemivariational problems with lack ofconvexity

-equations, using tools from Morse theory, we show the existence of four nontrivial solutions, all with sign information. Finally, for a special class of parametric equations, we obtain multiplicity theorems that substantially extend earlier results on the subject.

Resonant Robin problems driven by the p-Laplacian plus an indefinite potential

In this work we obtain an existence result for a class of singular quasilinear elliptic Dirichlet problems on a smooth bounded domain containing the origin. By using a Caffarelli-Kohn-Nirenberg type inequality, a critical point result for differentiable functionals is exploited, in order to prove the existence of a precise open interval of positive eigenvalues for which the treated problem admits at least one nontrivial weak solution. In the case of terms with a sublinear growth near the origin, we deduce the existence of solutions for small positive values of the parameter. Moreover, the corresponding solutions have smaller and smaller energies as the parameter goes to zero.

Nonlocal critical equations with concave-convex nonlinearities

Abstract We establish existence results of Hartmann–Stampacchia type for a class of variational–hemivariational inequalities on closed and convex sets (either bounded or unbounded) in a Hilbert space.

The critical equation in the resonant case

We consider a nonlinear Robin problems driven by the

Variational methods for nonlocal fractional problems

p

Multiplicity of solutions for Robin problems with double resonance

-Laplacian plus an indefinite potential. The reaction is resonant with respect to a variational eigenvalue. For the principal eigenvalue we assume strong resonance. Using variational tools and critical groups we prove existence and multiplicity theorems.