Investigation and solution of boundary-value problems with parameters by numerical-analytic method

Ronto, N. I.; Korol, Ihor

doi:10.1007/bf01056174

Cited by 4 publications

(2 citation statements)

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“…The boundary value problems with parameters both in the non-linear differential equations and in the linear boundary boundary conditions were investigated in [8], [9], [10], [11], [12], [13] by using the so called numerical-analytic method based upon successive approximations [8], [13].…”

Section: Introductionmentioning

confidence: 99%

“…n , Ax(0) + λCx(T ) = d, det C = 0, λ ∈ R, x 1 (0) = x 10 ,the PBVPs with nonfixed right boundary :     dx dt = f (t, x), t ∈ [0, λ], x, f ∈ R n , Ax(0) + Cx(λ) = d, det C = 0, λ ∈ (0, T ], x 1 (0) = x 10 , t, x), t ∈ [0, λ 2 ], x, f ∈ R n , λ 1 Ax(0) + Cx(λ 2 ) = d, det C = 0, λ 1 ∈ R, λ 2 ∈ (0, T ], x 1 (0) = x 10 , x 2 (0) = x 20 , and the PBVP of form  t, x), t ∈ [0, T ], x, f ∈ R n , λ 1 Ax(0) + λ 2 Cx(T ) = d, det C = 0, λ 1 , λ 2 ∈ R, x 1 (0) = x 10 , x 2 (0) = x 20 ,The paper[9] deals with the two-point PBVP     dx dt = f (t, x) + λ 1 g(t, x), t ∈ [0, T ], x, f ∈ R n , Ax(0) + λ 2 Cx(T ) = d, det C = 0, λ 1 , λ 2 ∈ R, x 1 (0) = x 10 , x 2 (0) = x 20 .…”

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On parametrized problems with non-linear boundary conditions

Rontó¹,

Shchobak²

2003

Proceedings of the 7'th Colloquium on the Qualitative Theory of Differential Equations (July 14--18, 2003, Szeged, Hungary) Edi

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We consider a parametrized boundary-value problem containing an unknown parameter both in the non-linear ordinary differential equations and in the non-linear boundary conditions. By using a suitable change of variables, we reduce the original problem to a family of those with linear boundary conditions plus some non-linear algebraic determining equations. We construct a numerical-analytic scheme suitable for studying the solutions of the transformed boundary-value problem. Acknowledgement 1. The first author was partially supported by the scholarship Charles Simonyi.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

On parametrized problems with non-linear boundary conditions

Rontó¹,

Shchobak²

2003

Proceedings of the 7'th Colloquium on the Qualitative Theory of Differential Equations (July 14--18, 2003, Szeged, Hungary) Edi

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Boundary-value problems with parameters for a multifrequency oscillation system

Самойленко

Petryshyn

1997

Ukr Math J

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By using the averaging method, we prove the solvability of boundary-value problems with parameters for nonlinear oscillation systems. We obtain estimates for the deviation of solutions of averaged problems from solutions of original problems. UDC 517.9We consider the following nonlinear system of ordinary differential equations:Its right-hand side is defined for (x, qo, % e)E D x R m x [0, L] x (0, e0] (here, eo << 1, D is a bounded domain of the real Euclidean space R~). We may take the functions a and b to have bounded continuous partial derivatives with respect to x, % and "c up to thesecond order and to be almost periodic in qo v, v = 1, m. We also assume that

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