Advanced differential equations with nonlinear boundary conditions

Jankowski, Tadeusz

doi:10.1016/j.jmaa.2004.09.059

Cited by 43 publications

(30 citation statements)

References 8 publications

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“…In this case for the validity it suffices to consider φ, ψ continuous functions, and the inequalities must be valid for every t ∈ I. We present an example which resembles some examples in [5,22]. Example 2.…”

Section: Examplesmentioning

confidence: 99%

“…As a consequence of the results in the previous sections (Theorems 2.7, 4.4), we analyze the following problem studied in [22].…”

Section: Example 411mentioning

confidence: 99%

“…Recently, the existence of solutions for advanced differential equations with nonlinear boundary conditions was studied in [22] by giving sufficient conditions for the uniqueness of solution or the existence of extremal solutions. As a particular case, the case of linear advanced differential inequalities is considered.…”

Section: Introductionmentioning

confidence: 99%

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Some considerations on functional differential equations of advanced type

Nieto

Rodríguez‐López

2010

Mathematische Nachrichten

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Key words Functional differential equation with advanced arguments, periodic boundary value problem, comparison results, uniqueness of solution MSC (2000) 34K10, 34K12, 34A40, 34B15We prove some comparison results for the periodic boundary value problem related to a first-order functional differential equation of advanced type. These maximum principles provide uniqueness results for nonlinear differential equations with advanced arguments. By a change of variable, we deduce analogous results for fuctional differential equations with delayed arguments.

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Section: Examplesmentioning

confidence: 99%

“…As a consequence of the results in the previous sections (Theorems 2.7, 4.4), we analyze the following problem studied in [22].…”

Section: Example 411mentioning

confidence: 99%

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Some considerations on functional differential equations of advanced type

Nieto

Rodríguez‐López

2010

Mathematische Nachrichten

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“…There is a vast literature devoted to the applications of this method to differential equations with initial and boundary conditions, for details, see [1,[4][5][6][7][8][9][10][11][15][16][17]. We also apply this technique to problem (1.1).…”

Section: Remarkmentioning

confidence: 99%

Integral boundary value problems for first order integro-differential equations with deviating arguments

Wang

Song

Zhang

2009

Journal of Computational and Applied Mathematics

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Integro-differential equations of mixed type Deviating arguments Integral boundary value conditions Monotone iterative technique Existence of solutions a b s t r a c t This paper deals with first order integro-differential equations of mixed type with deviating arguments. We investigate the existence of solutions of such problems with integral boundary conditions by establishing a comparison result and applying the monotone iterative technique. To obtain corresponding results, we also discuss first order differential inequalities with deviating arguments. Two examples demonstrate the application of our results.

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“…The monotone iterative method is useful to obtain approximate solutions of nonlinear differential equations, for details see for example [9], see also [1][2][3][4][5][6][7], [10,11].…”

Section: Introductionmentioning

confidence: 99%