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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 4, 2000, pp. 1035–1046
DOI: 10.4171/ZAA/996

Published online: 2000-12-31

A Nonlinear Boundary Value Problem for a Nonlinear Ordinary Differential Operator in Weighted Sobolev Spaces

Nguyen Thanh Long[1], Bui Tien Dung[2] and Ha Duy Hung[3]

(1) Polytechnic University of Ho Chi Minh City, Vietnam
(2) University of Ho Chi Minh City, Vietnam
(3) Faculty of Mathematics and Statistics, Ho Chi Minh City, Vietnam

We use the Calerkin and compactness method in appropriate weighted Sobolev spaces to prove the existence of a unique weak solution of the nonlinear boundary valued problem $$– \frac {1}{x^{\gamma}} \frac {d}{dx} M (x,u'(x)) + f(x,u(x)) = F(x) \ \ (0< x < 1)$$ $$| \mathrm {lim}_{x \to 0} + x^{\gamma / p} u'(x)| < + \infty$$ $$M(l,u'(1)) + h(u(l)) = 0$$ where $\gamma > 0, p > 2$ are given constants and $f, F, h, M$ are given functions.

Keywords: Boundary value problems, ordinary differential operators, weak solutions, existence and uniqueness, Galerkin method, weighted Sobolev spaces

Long Nguyen Thanh, Dung Bui Tien, Hung Ha Duy: A Nonlinear Boundary Value Problem for a Nonlinear Ordinary Differential Operator in Weighted Sobolev Spaces. Z. Anal. Anwend. 19 (2000), 1035-1046. doi: 10.4171/ZAA/996