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.

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

Nguyen Thanh Long

Bui Tien Dung

Ha Duy Hung

Abstract

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