A singular nonlinear boundary value problem in the nonlinear circular membrane under normal pressure

Abstract

The nonlinear boundary value problem $$ y" = f(x, y, y') = -\frac{x}{3}y' - \frac{y^2}{g(x)}, 0 < x < 1, $$ $$ (1.1) y'(0) = 0, and either (H) : y(1) = \lambda > 0 $$ $$ or (S) : y'(1) + (1 - \upsilon)y(1) = 0, 1 - \upsilon > 0, $$ $$g \in C[0, 1], k \leq g(x) \leq K on [0, 1] for some k, K > 0 $$ arises in the nonlinear circular membrane under normal pressure [2, 3]., 3].

Keywords

• Singlular boundary value problem;
• upper and lower solutions