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

Nguyen Thanh Long; Bui Tien Dung; Ha Duy Hung

doi:10.4171/zaa/996

JournalszaaVol. 19, No. 4pp. 1035–1046

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

Nguyen Thanh Long
Polytechnic University of Ho Chi Minh City, Vietnam
Bui Tien Dung
University of Ho Chi Minh City, Vietnam
Ha Duy Hung
Faculty of Mathematics and Statistics, Ho Chi Minh City, Vietnam

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Abstract

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 ^{γ}} \frac{d}{d x} M (x, u^{'} (x)) + f (x, u (x)) = F (x) (0 < x < 1)

∣ lim_{x \to 0} + x^{γ / p} u^{'} (x) ∣ < + \infty

M (l, u^{'} (1)) + h (u (l)) = 0

where $γ > 0, p > 2$ are given constants and $f, F, h, M$ are given functions.

Cite this article

Nguyen Thanh Long, Bui Tien Dung, Ha Duy Hung, A Nonlinear Boundary Value Problem for a Nonlinear Ordinary Differential Operator in Weighted Sobolev Spaces. Z. Anal. Anwend. 19 (2000), no. 4, pp. 1035–1046

DOI 10.4171/ZAA/996