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Nonlocal four-point boundary value problem for the singularly perturbed semilinear differential equations. (English) Zbl 1209.34018

Summary: This paper deals with the existence and asymptotic behavior of the solutions to singularly perturbed second-order nonlinear differential equations. We show that the solutions, in general, start with a fast transient which is the so-called boundary layer phenomenon, and after the decay of this transient they remain close to the solution of the reduced problem with an arising new fast transient at the end of the considered interval. Our analysis relies on the method of lower and upper solutions.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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References:

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