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

Nguyen Thanh Long; Bui Tien Dung; Tran Minh Thuyet

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
Tran Minh Thuyet
Vietnam National University of Ho Chi Minh City, Vietnam

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Abstract

We use the Galerkin 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, Tran Minh Thuyet, 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