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Ekeland's variational principle in locally p-convex spaces and related results

J. H. Qiu, S. Rolewicz (2008)

Studia Mathematica

In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.

Equilibrium of maximal monotone operator in a given set

Dariusz Zagrodny (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms

Thomas Lorenz (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarly to quasidifferential equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. In spite of lacking any linear structures, a distribution-like approach leads to so-called right-hand forward solutions. These extensions are mainly motivated by compact subsets of the Euclidean space...

Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

Truong Q. Bao, Boris S. Mordukhovich (2007)

Applications of Mathematics

In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form 0 G ( x ) + Q ( x ) , where both G and Q 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 solutions and of multiple solutions for nonlinear nonsmooth periodic systems

Evgenia H. Papageorgiou, Nikolaos S. Papageorgiou (2004)

Czechoslovak Mathematical Journal

In this paper we examine nonlinear periodic systems driven by the vectorial p -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. p = 2 ) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem...

Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side

Hôǹg Thái Nguyêñ, Dariusz Pączka (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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...

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