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A generalized quasilinearization technique is applied to obtain a sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with nonlocal discontinuous type integral boundary conditions.

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 problem with an inner point for the singularly perturbed semilinear differential equations

Róbert Vrábeľ (2011)

Mathematica Bohemica

In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $ϵ y^{''} + k y = f (t, y), t \in 〈 a, b 〉, k < 0, 0 < ϵ ≪ 1$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.

Boundary value problems for generalized linear differential equations

Štefan Schwabik, Milan Tvrdý (1979)

Czechoslovak Mathematical Journal

Boundary value problems for generalized linear integrodifferential equations with left-continuous solutions

Milan Tvrdý (1974)

Časopis pro pěstování matematiky

Boundary value problems for higher order ordinary differential equations

Armando Majorana, Salvatore A. Marano (1994)

Commentationes Mathematicae Universitatis Carolinae

Let $f : [a, b] \times ℝ^{n + 1} \to ℝ$ be a Carath’eodory’s function. Let ${t_{h}}$ , with $t_{h} \in [a, b]$ , and ${x_{h}}$ be two real sequences. In this paper, the family of boundary value problems $\{\begin{matrix} x^{(k)} = f (t, x, x^{'}, ..., x^{(n)}) x^{(i)} (t_{i}) = x_{i}, i = 0, 1, ..., k - 1 \end{matrix} (k = n + 1, n + 2, n + 3, ...)$ is considered. It is proved that these boundary value problems admit at least a solution for each $k \geq ν$ , where $ν \geq n + 1$ 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.

Boundary value problems for linear differential equations of operators

I. E. Sharkawi (1977)

Matematički Vesnik

Boundary value problems for third order differential equations by solution matching.

Henderson, Johnny (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Boundary value problems with bounded $ϕ$ -Laplacian and nonlocal conditions of integral type

Daria Bugajewska, Jean Mawhin (2025)

Czechoslovak Mathematical Journal

We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded $ϕ$ -Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.