Generalized upper and lower solution method for the forced Duffing equation

Wang, Chengwen

doi:10.1090/s0002-9939-97-03947-6

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1998

2022

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Cited by 7 publications

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“…As a method to study the characterizes of solutions, the upper and lower approach has been attracted much attention from a lot of researchers for many years, see [3,16,26,27,28] and references therein. Motivated by one of those papers, which establish the monotone methods in nonlinear elliptic and parabolic boundary value problems [27].…”

Section: Introductionmentioning

confidence: 99%

Monotone methods for semilinear parabolic and elliptic equations on graphs

Hu¹,

Lei²

2022

Preprint

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This paper is devoted to investigate the extinction and propagation properties of the solutions to the graph Laplacian parabolic problems with nonlinear reaction terms on networks. To this end, we establish the (strong) maximum principle for the parabolic and elliptic problems on networks. The stability of the solutions is studied by using the upper and lower solutions method to construct suitable iterative sequence. Moreover, we give examples as the application of this technique.

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Section: Introductionmentioning

confidence: 99%