Solvability of Nonlinear Singular Problems for Ordinary Differential Equations

Rachůnková, Irena; Staněk, Svatoslav; Tvrdý, Milan

doi:10.1155/9789774540400

Cited by 45 publications

(34 citation statements)

References 146 publications

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“…Otherwise 0 is a singular point of the ODE. On the other hand, if ( ) or ( ) are not analytic at 0 , then 0 is said to be a singular point [14,15].…”

Section: Singular Boundary Value Problemmentioning

confidence: 99%

Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Tawfiq

Hussein

2013

ISRN Applied Mathematics

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The aim of this paper is to design feed forward neural network for solving second-order singular boundary value problems in ordinary differential equations. The neural networks use the principle of back propagation with different training algorithms such as quasi-Newton, Levenberg-Marquardt, and Bayesian Regulation. Two examples are considered to show that effectiveness of using the network techniques for solving this type of equations. The convergence properties of the technique and accuracy of the interpolation technique are considered.

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“…Otherwise 0 is a singular point of the ODE. On the other hand, if ( ) or ( ) are not analytic at 0 , then 0 is said to be a singular point [14,15].…”

Section: Singular Boundary Value Problemmentioning

confidence: 99%

Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Tawfiq

Hussein

2013

ISRN Applied Mathematics

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“…For rather representative overview and references, see e.g. [15] or [16]. To our knowledge, up to now singular periodic impulsive problems have not been treated.…”

Section: Preliminariesmentioning

confidence: 99%

Singular periodic impulse problems

Halas

Tvrdý

2008

Nonlinear Oscill

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Abstract.Existence principle for the impulsive periodic boundary value problem u + c u = g(x) + e(t), u(is established, where g ∈ C(0, ∞) can have a strong singularity at the origin. Furthermore, we assume that 0 < t 1 < . .The principle is based on an averaging procedure similar to that introduced by Manásevich and Mawhin for singular periodic problems with p -Laplacian in [11]. Mathematics Subject Classification 2000. 34B37, 34B15, 34C25 Keywords. impulses, periodic solutions, topological degree PreliminariesStarting with Hu and Lakshmikantham [7], periodic boundary value problems for nonlinear second order impulsive differential equations of the formhave been studied by many authors. Usually it is assumed that the function f : [0, T ] × R 2 → R fulfils the Carathéodory conditions, 0 < t 1 < t 2 < . . . < t m < T are fixed points of the interval [0, T ] (1.4) 1

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“…For other results on the existence of positive solutions of singular nonlinear Neumann problems, see Rachunková, Staněk and Tvrdý [9], Sun, Cho and O'Regan [12], Chu, Sun and Chen [1], Li [5], and Li and Jiang [4].…”

Section: Introductionmentioning

confidence: 99%

Existence of one-signed solutions of nonlinear four-point boundary value problems

Chen

2012

Czech Math J

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Solvability of Nonlinear Singular Problems for Ordinary Differential Equations

Cited by 45 publications

References 146 publications

Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Design Feed Forward Neural Network to Solve Singular Boundary Value Problems

Singular periodic impulse problems

Existence of one-signed solutions of nonlinear four-point boundary value problems

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