Existence and uniqueness of extremal mild solutions for non-autonomous nonlocal integro-differential equations via monotone iterative technique

Meraj, Arshi; Pandey, Dwijendra N.

doi:10.2298/fil1910985m

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…In [10], the authors considered the existence and uniqueness of maxinal mild solutions for non-autonomous integro-differential equations having nonlocal condition. They applied a monotone iterative method with upper and lower solutions in an ordered Banach space X combined with evolution system and measure of noncompactness.…”

Section: Introductionmentioning

confidence: 99%

On maximal solution to a degenerate parabolic equation involving in time fractional derivative

Dai Nghia,

Hoang Luc,

Qin

et al. 2023

Electron. J. Appl. Math.

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In this paper, we consider a degenerate parabolic equation associated with Caputo derivative. Our problem is studied in the unbounded domain and the nonlocal initial condition. Under some suitable conditions of the input data, we show the local existence of the mild solution. Then we show the continuation of the mild solution. We also claim the maximal mild solution. The main analysis in the current paper is based on some estimations of resolvent theory combined with many complex valuations on solutions operators in Banach spaces.

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Section: Introductionmentioning

confidence: 99%

On maximal solution to a degenerate parabolic equation involving in time fractional derivative

Dai Nghia,

Hoang Luc,

Qin

et al. 2023

Electron. J. Appl. Math.

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Existence of solutions of non-autonomous fractional differential equations with integral impulse condition

Kumar¹,

Chauhan

Ravichandran³

et al. 2020

Adv Differ Equ

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Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions

Zhu

2023

Filomat

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In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which the undelayed part admits an evolution operator. We discuss the problems by utilizing theory of evolution operators, Schauder fixed point theorem and Banach fixed point theorem. Some new results on existence and uniqueness of solutions of the considered equation are obtained on the infinite internal [0,+?). In the end, the obtained results are applied to a class of non-autonomous heat equations with state-dependent nonlocal conditions.

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Existence and uniqueness of extremal mild solutions for non-autonomous nonlocal integro-differential equations via monotone iterative technique

Cited by 3 publications

References 18 publications

On maximal solution to a degenerate parabolic equation involving in time fractional derivative

On maximal solution to a degenerate parabolic equation involving in time fractional derivative

Existence of solutions of non-autonomous fractional differential equations with integral impulse condition

Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions

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