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Boundary layer phenomenon for three -point boundary value problem for the nonlinear singularly perturbed systems

Robert Vrabel (2011)

Kybernetika

This paper deals with the three-point boundary value problem for the nonlinear singularly perturbed second-order systems. Especially, we focus on an analysis of the solutions in the right endpoint of considered interval from an appearance of the boundary layer point of view. We use the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear systems considered here.

Boundary problems for generalized Lyapunov equations.

Lucas Jódar Sánchez (1986)

Stochastica

Boundary value problems for generalized Lyapunov equations whose coefficients are time-dependant bounded linear operators defined on a separable complex Hilbert space are studied. Necessary and sufficient conditions for the existence of solutions and explicit expressions of them are given.

Boundary value problems for higher order ordinary differential equations

Armando Majorana, Salvatore A. Marano (1994)

Commentationes Mathematicae Universitatis Carolinae

Let f : [ a , b ] × n + 1 be a Carath’eodory’s function. Let { t h } , with t h [ a , b ] , and { x h } be two real sequences. In this paper, the family of boundary value problems x ( k ) = f t , x , x ' , ... , x ( n ) x ( i ) ( t i ) = x i , i = 0 , 1 , ... , k - 1 ( k = n + 1 , n + 2 , n + 3 , ... ) is considered. It is proved that these boundary value problems admit at least a solution for each k ν , where ν n + 1 is a suitable integer. Some particular cases, obtained by specializing the sequence { t h } , are pointed out. Similar results are also proved for the Picard problem.

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