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Boundary value problems with nonlinear conditions. (English) Zbl 0854.34025
The paper is devoted to the boundary value problem $$x''= f(t, x, x')$$, $$g_1(x(a), x'(a))= 0$$, $$g_2(x(b), x'(b))= 0$$, where $$-\infty< a< b< \infty$$, $$f: [a, b]\times \mathbb{R}^2\to \mathbb{R}$$ satisfies the Carathéodory conditions and the mappings $$g_i: \mathbb{R}^2\to \mathbb{R}$$, $$i= 1,2$$, are continuous and in general nonlinear. Making use of the topological degree method and the upper and lower solutions method, the author proves several theorems on the existence of solutions for the cases when neither monotonicity of $$g_1$$, $$g_2$$ nor growth conditions for $$f$$ are required.
Reviewer: M.Tvrdý (Praha)

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations
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##### References:
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