2007Journal of Naval University of EngineeringRequires access

Oscillation criteria of nonlinear parabolic partial functional differential equations with continuous distribution delay

Luo Li-ping

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Abstract

The oscillation of a class of nonlinear parabolic partial functional differential equations with continuous distribution delay is considered in this paper.To reduce the multi-dimensional oscillation problems to one-dimensional problems for certain nonlinear differential inequalities with continuous distribution delay by employing Green′s theorem,some sufficient criteria are proposed for oscillation of all solutions of such equations under Robin and Dirichlet boundary value conditions.The conclusion fully indicates that the oscillation is caused by delay.

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The oscillation of a class of nonlinear parabolic partial functional differential equations with continuous distribution delay is considered in this paper.To reduce the multi-dimensional oscillation problems to one-dimensional problems for certain nonlinear differential inequalities with continuous distribution delay by employing Green′s theorem,some sufficient criteria are proposed for oscillation of all solutions of such equations under Robin and Dirichlet boundary value conditions.The conclusion fully indicates that the oscillation is caused by delay.

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Available abstract

The oscillation of a class of nonlinear parabolic partial functional differential equations with continuous distribution delay is considered in this paper.To reduce the multi-dimensional oscillation problems to one-dimensional problems for certain nonlinear differential inequalities with continuous distribution delay by employing Green′s theorem,some sufficient criteria are proposed for oscillation of all solutions of such equations under Robin and Dirichlet boundary value conditions.The conclusion fully indicates that the oscillation is caused by delay.

Key concepts: Oscillation (cell signaling), Mathematics, Nonlinear system, Mathematical analysis, Delay differential equation, Boundary value problem, Partial differential equation, Distribution (mathematics)

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