Euler-Lagrange inclusions and existence of minimizers for a class of non-coercive variational problems.
Existence and multiplicity of solutions for a differential inclusion problem involving the -Laplacian.
Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Existence of a renormalized solution of nonlinear degenerate elliptic problems
We study a general class of nonlinear elliptic problems associated with the differential inclusion in Ω where . The vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general -data.
Existence of extremal periodic solutions for nonlinear evolution inclusions
We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.
Existence results for the equation in .
Existence theorems for a semilinear elliptic boundary value problem
Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side
We present two existence results for the Dirichlet elliptic inclusion with an upper semicontinuous multivalued right-hand side in exponential-type Orlicz spaces involving a vector Laplacian, subject to Dirichlet boundary conditions on a domain Ω⊂ ℝ². The first result is obtained via the multivalued version of the Leray-Schauder principle together with the Nakano-Dieudonné sequential weak compactness criterion. The second result is obtained by using the nonsmooth variational technique together with...
Existence theory for perturbed hyperbolic differential inclusions.
Galerkin approximations for nonlinear evolution inclusions
In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.
Generalized gradients for locally Lipschitz integral functionals on non--type spaces of measurable functions
Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put . Consider the integral functional G defined on some non--type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...
Indépendance des fréquences par rapport aux solutions quasi- periodiques de certaines équations d'evolution non linéaires.
Iterative methods for the Darboux problem for partial functional differential equations.
Local solvability of a constrained gradient system of total variation.
Multivalued nonpositone problems
In this note, the existence of non-negative solutions for some multivalued non-positone elliptic problems is studied.
New existence and stability results for partial fractional differential inclusions with multiple delay
We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.
Nonconvex evolution inclusions generated by time-dependent subdifferential operators.
Non-degenerate implicit evolution inclusions.
Nonlinear elliptic differential equations with multivalued nonlinearities
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper...
Nonlinear evolution equations generated by subdifferentials with nonlocal constraints
We consider an abstract formulation for a class of parabolic quasi-variational inequalities or quasi-linear PDEs, which are generated by subdifferentials of convex functions with various nonlocal constraints depending on the unknown functions. In this paper we specify a class of convex functions on a real Hilbert space H, with parameters 0 ≤ t ≤ T and v in a set of functions from [-δ₀,T], 0 < δ₀ < ∞, into H, in order to formulate an evolution equation of the form , 0 < t < T, in H. Our...