## Nonnegative solutions to superlinear problems of generalized Gelfand type.(English)Zbl 0831.34029

The author considers the existence of nonnegative solutions of the boundary value problems $$y'' + \mu q(t) g(t,y) = 0$$, $$\mu \geq 0$$, a) $$y(0) = a \geq 0$$, $$y(T) = b \geq a$$ or b) $$y(0) = a \geq 0$$, $$y$$ bounded on $$[0, \infty)$$ or c) $$y(0) = a \geq 0$$, $$\lim y (t)$$ for $$t \to \infty$$ exists. The main assumptions are the following: $$q(t) > 0$$ continuous on $$(0,T)$$, $$g(t,y)$$ continuous, nonnegative on $$[0,T] \times [a, \infty)$$ or on $$[0, \infty) \times [a, \infty)$$, respectively, $$f : [0, \infty) \to [0, \infty)$$ continuous nondecreasing, $$f(u) > 0$$ for $$u > a$$ and $$g(t,u) \leq f(u)$$. The proofs are made via fixed point theorem (nonlinear alternative).

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: