Aurelian Cernea (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We prove the existence of viable solutions to the Cauchy problem x” ∈ F(x,x’), x(0) = x₀, x’(0) = y₀, where F is a set-valued map defined on a locally compact set , contained in the Fréchet subdifferential of a ϕ-convex function of order two.
Pavel Krejčí, Philippe Laurençot (2002)
Bollettino dell'Unione Matematica Italiana
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We define a mapping which with each function and an admissible value of associates the function with a prescribed initial condition which minimizes the total variation in the -neighborhood of in each subinterval of . We show that this mapping is non-expansive with respect to , and , and coincides with the so-called play operator if is a regulated function.
Márton Elekes, András Máthé (2009)
Fundamenta Mathematicae
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A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also...
Viorel Barbu, Angelo Favini (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We prove two existence results on abstract differential equations of the type and we give some applications of them to partial differential equations.
Ralf Bader, Nikolaos S. Papageorgiou (2001)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when and , with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
P. Courilleau, S. Fabre, J. Mossino (2001)
Bollettino dell'Unione Matematica Italiana
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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo in un dominio limitato dello spazio -dimensionale; e sono matrici con coefficenti limitati, e è invertibile e la sua matrice inversa ha anche coefficenti limitati. La non linearità è dovuta alla funzione ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul -Laplaciano, , ed assicurano l'esistenza di...
Kaori Yamazaki (2010)
Studia Mathematica
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Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer...
Sahbi Boussandel (2018)
Applications of Mathematics
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The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet -Laplace operator.