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On a boundary value problem in nonlinear mechanics. (Sur un problème aux limites en mécanique non linéaire.) (French) Zbl 0839.34030
The paper deals with a boundary value problem arising in nonlinear mechanics, (1) $$y'' = - (k/y^2) - 3y'/x$$, $$0 < x \leq 1$$, $$y(1) = \lambda$$, $$y'(0) = 0$$, $$y(0)$$ is regular. Here $$\lambda$$ and $$k$$ are positive constants. The author transforms (1) into an asymptotic problem on the half-line and then, using the upper and lower solutions method and the existence result by A. Granas, R. B. Guenther, J. W. Lee and D. O’Regan [J. Math. Anal. Appl. 116, 335-348 (1986; Zbl 0594.34019)] he proves the existence of a solution of (1).

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 74K20 Plates 34C11 Growth and boundedness of solutions to ordinary differential equations