Sign conditions in nonlinear boundary value problems.(English)Zbl 0845.34036

Summary: We consider the second-order differential equation $$x''= f(t, x, x')$$ with a Carathéodory nonlinearity $$f$$ and nonlinear boundary conditions $$g_1(x(a), x'(a))= 0$$, $$g_2(x(b), x'(b))= 0$$. Using the topological degree method we prove the existence of solutions provided $$f$$, $$g_1$$, $$g_2$$ satisfy appropriate sign conditions.

MSC:

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

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