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This paper establishes oscillation theorems for a class of functional parabolic equations which arises from logistic population models with delays and diffusion.

Oscillation of Bôcher's pairs with respect to halflinear second order diff. equ.-s

Bihari, Imre (1982)

Equadiff 5

Oscillation of nonlinear impulsive hyperbolic equations with several delays.

Liu, Anping, Li, Xiao, Liu, Ting (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions for forced nonlinear neutral hyperbolic equations with functional arguments.

Shoukaku, Yutaka (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions for systems of hyperbolic equations of neutral type.

Wang, Peiguang, Wu, Yonghong (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions to a higher-order neutral PDE with distributed deviating arguments.

Dix, J.G. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillation of systems of certain neutral delay parabolic differential equations.

Li, Wei Nian, Cui, Bao Tong, Debnath, Lokenath (2003)

Journal of Applied Mathematics and Stochastic Analysis

Oscillation of the solution to a singular differential equation.

Kurepa, Alexandra, Weithers, Hugh (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation properties for parabolic equations of neutral type

Bao Tong Cui (1992)

Commentationes Mathematicae Universitatis Carolinae

The oscillation of the solutions of linear parabolic differential equations with deviating arguments are studied and sufficient conditions that all solutions of boundary value problems are oscillatory in a cylindrical domain are given.

Oscillation theorems and nodes of eigenfunctions of certain differential equations of the fourth order

Jan Bochenek (1972)

Annales Polonici Mathematici

Oscillation theory of higher-order ordinary and functional differential equations with forcing terms

Kusano, Takaŝi (1982)

Equadiff 5

Oscillation theory of self-adjoint equations and some its applications

Došlý, Ondřej (1994)

Equadiff 8

Oscillations and concentrations generated by $𝒜$ -free mappings and weak lower semicontinuity of integral functionals

Irene Fonseca, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

DiPerna's and Majda's generalization of Young measures is used to describe oscillations and concentrations in sequences of maps ${u_{k}}_{k \in ℕ} \subset L^{p} (Ω; ℝ^{m})$ satisfying a linear differential constraint $𝒜 u_{k} = 0$ . Applications to sequential weak lower semicontinuity of integral functionals on $𝒜$ -free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det $\nabla ϕ_{k} \overset{*}{⇀} \det \nabla ϕ$ in measures on the closure of $Ω \subset ℝ^{n}$ if $ϕ_{k} ⇀ ϕ$ in $W^{1, n} (Ω; ℝ^{n})$ . This convergence holds, for example, under...

Oscillations and concentrations in sequences of gradients

Martin Kružík, Agnieszka Kałamajska (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ø; ℝ^{m \times n})$ if $p > 1$ and $Ω \subset ℝ^{n}$ is a bounded domain with the extension property in $W^{1, p}$ . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of $Ω$ are required and links with lower semicontinuity results...

Oscillations and concentrations in sequences of gradients

Agnieszka Kałamajska, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ω; ℝ^{m \times n})$ if p > 1 and $Ω \subset ℝ^{n}$ is a bounded domain with the extension property in $W^{1, p}$ . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of Ω are required and links with lower semicontinuity...

Oscillations fortes sur un champ linéairement dégénéré

Christophe Cheverry, Olivier Guès, Guy Métivier (2003)

Annales scientifiques de l'École Normale Supérieure

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