Displaying similar documents to “On a nonlinear compactness lemma in L p ( 0 , T ; B ) .”

Existence of solutions for a class of second-order p -Laplacian systems with impulsive effects

Peng Chen, Xianhua Tang (2014)

Applications of Mathematics

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The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system d d t ( | u ˙ ( t ) | p - 2 u ˙ ( t ) ) = ∇ F ( t , u ( t ) ) , a.e. t ∈ [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 , Δ u ˙ i ( t j ) = u ˙ i ( t j + ) - u ˙ i ( t j - ) = I i j ( u i ( t j ) ) , i = 1 , 2 , ⋯ , N ; j = 1 , 2 , ⋯ , m . By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order p -Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.

Optimal time and space regularity for solutions of degenerate differential equations

Alberto Favaron (2009)

Open Mathematics

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We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.

Reliable solution of parabolic obstacle problems with respect to uncertain data

Ján Lovíšek (2003)

Applications of Mathematics

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A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier...

Existence of weak solutions to doubly degenerate diffusion equations

Aleš Matas, Jochen Merker (2012)

Applications of Mathematics

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We prove existence of weak solutions to doubly degenerate diffusion equations u ˙ = Δ p u m - 1 + f ( m , p ≥ 2 ) by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains Ω ⊂ ℝ n with Dirichlet or Neumann boundary conditions. The function f can be an inhomogeneity or a nonlinearity involving terms of the form f ( u ) or div ( F ( u ) ) . In the appendix, an introduction to weak...