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

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

1xγddxM(x,u(x))+f(x,u(x))=F(x)  (0<x<1)– \frac {1}{x^{\gamma}} \frac {d}{dx} M (x,u'(x)) + f(x,u(x)) = F(x) \ \ (0< x < 1)
limx0+xγ/pu(x)<+| \mathrm {lim}_{x \to 0} + x^{\gamma / p} u'(x)| < + \infty
M(l,u(1))+h(u(l))=0M(l,u'(1)) + h(u(l)) = 0

where γ>0,p>2\gamma > 0, p > 2 are given constants and f,F,h,Mf, 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