Displaying similar documents to “On some semilinear Volterra diffusion equations arising in ecology”

New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations

Mimia Benhadri, Tomás Caraballo (2022)

Mathematica Bohemica

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This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.

L 2 -stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s

Salvatore Rionero (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The L 2 -stability (instability) of a binary nonlinear reaction diffusion system of P.D.E.s - either under Dirichlet or Neumann boundary data - is considered. Conditions allowing the reduction to a stability (instability) problem for a linear binary system of O.D.E.s are furnished. A peculiar Liapunov functional V linked (together with the time derivative along the solutions) by direct simple relations to the eigenvalues, is used.