Sign changing periodic solutions for the Chafee–Infante equation

Huang, Haochuan; Huang, Rui

doi:10.1080/00036811.2017.1359570

Cited by 7 publications

(2 citation statements)

References 20 publications

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“…is known as the Chafee -Infante equation, see e.g. Huang and Huang [69], named after original important work on bifucation by Chafee [70] and Chafee and Infante [71,72].…”

Section: The Chafee -Infante Equationmentioning

confidence: 99%

Jordan–Cattaneo waves: Analogues of compressible flow

Straughan

2020

Wave Motion

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“…is known as the Chafee -Infante equation, see e.g. Huang and Huang [69], named after original important work on bifucation by Chafee [70] and Chafee and Infante [71,72].…”

Section: The Chafee -Infante Equationmentioning

confidence: 99%

Jordan–Cattaneo waves: Analogues of compressible flow

Straughan

2020

Wave Motion

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“…Henry investigated the problem of existence of solutions as well as equilibria for two alleles in the case of homogeneous, isotropic migration (corresponding to the Laplacian). Since then, the problem was extended by many authors, for instance, Lou and Nagylaki in [26] considered the case of multiple alleles and of arbitrary migration (corresponding to an arbitrary elliptic operator); Huang and Huang in [17] consider (1.1) with h(t, x, u) = λ(t)(u − u 3 ) and prove the existence of periodic mild solutions; Viorel in [33] studies (1.1) with Neumann boundary conditions, combined to an integral-type nonlocal initial condition and proves the existence of global solutions near asymptotically stable equilibrium points. We associate to the above equation a general nonlocal initial condition:…”

Section: Introductionmentioning

confidence: 99%

Evolution equations with nonlocal initial conditions and superlinear growth

Benedetti¹,

Ciani²

2021

Preprint

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We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as particular cases, the Cauchy multipoint problem, the weighted mean value problem and the periodic problem. The dynamic is transformed into an abstract setting and by combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results. By the compactness of the semigroup generated by the linear operator, we do not assume any Lipschitzianity, nor compactness on the nonlinear term or on the nonlocal initial condition. In addition, the exploited approximation technique coupled to a Hartman-type inequality argument, allows to treat nonlinearities with superlinear growth. Moreover, regarding the periodic case we are able to prove the existence of at least one periodic solution on the half line.

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Asymptotic Behavior of Solutions for the Chafee-Infante Equation

Huang

2020

Acta Math Sci

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Sign changing periodic solutions for the Chafee–Infante equation

Cited by 7 publications

References 20 publications

Jordan–Cattaneo waves: Analogues of compressible flow

Jordan–Cattaneo waves: Analogues of compressible flow

Evolution equations with nonlocal initial conditions and superlinear growth

Asymptotic Behavior of Solutions for the Chafee-Infante Equation

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