Existence of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions

Chen, Pengyu; Li, Yongxiang; Fan, Hong-Yi

doi:10.1186/1687-1847-2012-79

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…For instance, Boucherif and Precup in [5] consider the multipoint condition under the assumption of the compactness of the semigroup generated by the linear part. In the same setting, see also [40] for functional semilinear differential equations and [8] for strong solutions. Paicu and Vrabie [28] consider a general nonlocal initial condition of type (1.2).…”

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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Section: Introductionmentioning

confidence: 99%

Evolution equations with nonlocal initial conditions and superlinear growth

Benedetti¹,

Ciani²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Agarwal [17], R.P. Agarwal, M. Benchohra, S. Hamani [18], P. Chen, Y. Li and H. Fan [19], Wahash-Panchal-Abdo [40], Ardjounia-Djoudi [41], etc. In [9], K. Balachandran and J.Y.…”

Section: Introductionmentioning

confidence: 99%

Existence of mild solutions to semilinear fractional evolution equation using Krasnoselskii fixed point theorem

Ngoc

Tuấn

2022

Filomat

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This paper is devoted to study the existence and stability of mild solutions for semilinear fractional evolution equations with a nonlocal final condition. The analysis is based on analytic semigroup theory, Krasnoselskii fixed point theorem, and a special probability density function. An application to a time fractional diffusion equation with nonlocal final condition is also given.

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Regularity results for some class of nonautonomous partial neutral functional differential equations with finite delay

Kyelem

2021

SeMA

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Existence of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions

Cited by 5 publications

References 21 publications

Evolution equations with nonlocal initial conditions and superlinear growth

Evolution equations with nonlocal initial conditions and superlinear growth

Existence of mild solutions to semilinear fractional evolution equation using Krasnoselskii fixed point theorem

Regularity results for some class of nonautonomous partial neutral functional differential equations with finite delay

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