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.


34B15 Nonlinear boundary value problems for ordinary differential equations
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