Global Existence for Semilinear Evolution Equations with Nonlocal Conditions

Ntouyas, Sotiris K.; Tsamatos, P. Ch.

doi:10.1006/jmaa.1997.5425

Cited by 151 publications

(77 citation statements)

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“…Closed form representation for Ker B(z) and the proposition of Theorem 1 guarantee that (17) forms a necessary and sufficient conditions for the existence of generalized solution to (15). Example 1 is instructive in a sense that, for such nonlocal problem, one can easily compare conditions (3) and (17) graphically. This comparison is given on Fig.…”

Section: Reduction Of Nonlocal Problem To Classical Cauchy Problemmentioning

confidence: 96%

“…While in reality the admissible set grows larger when we make θ smaller. Check, for example, the corresponding set for the case θ = π/6 obtained using (17) which is coloured in light grey on Fig. 1.…”

Section: Reduction Of Nonlocal Problem To Classical Cauchy Problemmentioning

confidence: 99%

“…Here we will introduce more advanced and yet quite straightforward technique for the treatment of nonlocal problems. To do that, in Section 2 we reduce the given problem (2) to the corresponding Cauchy problem with ordinary initial value condition as in [12,17]. The subsequent analysis, presented in Section 3, study the correctness of the solution operator defined via the Dunford-Cauchy formula on a feasible integration contour.…”

Section: Introductionmentioning

confidence: 99%

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Existence of the solution to a nonlocal-in-time evolutional problem

Макаров

Sytnyk

Vasylyk

2014

NAMC

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Abstract. This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal problem to its classical initial value analogue, uses more advanced analysis. That is a validation of the correctness in definition of the general solution representation via the Dunford-Cauchy formula. Such approach allows us to reduce the given existence problem to the problem of locating zeros of a certain entire function. It results in the necessary and sufficient conditions for the existence of a generalized (mild) solution to the given nonlocal problem. Aside of that we also present new sufficient conditions which in the majority of cases generalize existing results.

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Section: Reduction Of Nonlocal Problem To Classical Cauchy Problemmentioning

confidence: 96%

Section: Reduction Of Nonlocal Problem To Classical Cauchy Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence of the solution to a nonlocal-in-time evolutional problem

Макаров

Sytnyk

Vasylyk

2014

NAMC

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“…Byszewski and Lakshmikanthan [9] proved an existence and uniqueness of solutions of a nonlocal Cauchy problem in Banach spaces. Ntouyas and Tsamatos [23] studied the existence for semilinear evolution equations with nonlocal conditions. The problem of existence of solutions of evolution equations in Banach space has been studied by several authors [3,12,24].…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for quasi-linear impulsive functional integrodifferential equations in Banach spaces

Samuel¹,

Balachandran²

2014

J. Nonlinear Sci. Appl.

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“…For the importance of nonlocal conditions in different fields, we refer the reader to [1][2][3], [4,10,[12][13][14][15] and the references contained therein. The integrodifferential equation with nonlocal conditions has been investigated extensively.…”

Section: Introductionmentioning

confidence: 99%

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

Yong-sheng¹,

Wang²

2011

OpMath

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Abstract. In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.

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Global Existence for Semilinear Evolution Equations with Nonlocal Conditions

Cited by 151 publications

References 1 publication

Existence of the solution to a nonlocal-in-time evolutional problem

Existence of the solution to a nonlocal-in-time evolutional problem

Existence of solutions for quasi-linear impulsive functional integrodifferential equations in Banach spaces

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

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