Oscillatory Solutions of Boundary Value Problems

Sadyrbaev, Felix

doi:10.1007/978-3-319-32857-7_11

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2017

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“…In the paper [9] a resonant problem for the second order nonlinear equation is treated from "inside". First the type of a solution is introduced.…”

Section: Introductionmentioning

confidence: 99%

On conversion of resonant problem to non-resonant one

Sveikate¹,

Sadyrbaev²

2017

MMN

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Abstract. We consider a nonlinear resonant boundary value problem. To prove the existence of a solution to a given boundary value problem we replace the linear part of a given equation by non-resonant linear part. First, to modify a resonant problem to a regular one we use the Taylor expansion for f .t; x; x 0 / with respect to x. The second way of conversion a given problem to nonresonant one is based on an appropriate choice of "good" approximation to expected solution. We provide the existence results illustrating both ways.

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“…In the paper [9] a resonant problem for the second order nonlinear equation is treated from "inside". First the type of a solution is introduced.…”

Section: Introductionmentioning

confidence: 99%