Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case
Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints
In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form where both and are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under...
Existence of minimizers for non-quasiconvex functionals arising in optimal design
Existence of minimizers for some non convex one-dimensional integrals.
Existence of minimizers of free autonomous variational problems via solvability of constrained ones
Existence of multiple solutions for quasilinear diagonal elliptic systems.
Existence of optimal controls for control systems governed by nonlinear partial differential equations
Existence of optimal maps in the reflector-type problems
In this paper, we consider probability measures μ and ν on a d-dimensional sphere in and cost functions of the form that generalize those arising in geometric optics where We prove that if μ and ν vanish on -rectifiable sets, if |l'(t)|>0, and is monotone then there exists a unique optimal map To that transports μ onto where optimality is measured against c. Furthermore, Our approach is based on direct variational arguments. In the special case when existence of optimal maps...
Existence of optimal nonanticipating controls in piecewise deterministic control problems
Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.
Existence of optimal solutions in general discrete systems
Existence of regular solutions for nonlinear Signorini's problem
Existence of solution a of nonlinear degenerate systems of parabolic variational inequalities
Existence of solutions and algorithm for a system of variational inequalities.
Existence of solutions and convergence of a multistep iterative algorithm for a system of variational inclusions with -accretive operators.
Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems
In this paper we examine nonlinear periodic systems driven by the vectorial -Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. ) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem...
Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces.
Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space.
Existence of solutions for some quasi-variational inequalities
Existence of solutions for the Dirichlet problem with superlinear nonlinearities
In this paper we establish the existence of nontrivial solutions to with superlinear in .
Existence of solutions for unilateral problems with multivalued operators.