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Existence of three-solutions for second-order differential equations with nonlinear boundary value conditions

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Abstract

The paper deals with the existence of three-solutions for the second-order differential equations with nonlinear boundary value conditions

$$\begin{gathered} x'' = f(t,x,x'), t \in \left[ {a,b} \right], \hfill \\ g_1 (x(a),x'(a)) = 0, g_2 (x(b), x'(b)) = 0, \hfill \\ \end{gathered} $$

where f:[a,b] × R 1 × R 1R 1, g i :R 1 × R 1R 1 (i=1,2) are continuous functions. The methods employed are the coincidence degree theory. As an application, the sufficient conditions under which there are arbitrary odd solutions for the BVP are obtained.

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Supported by the Postdoctor Science Foundation of China (200114).

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Liu, B. Existence of three-solutions for second-order differential equations with nonlinear boundary value conditions. Appl. Math. Chin. Univ. 17, 135–144 (2002). https://doi.org/10.1007/s11766-002-0037-3

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  • DOI: https://doi.org/10.1007/s11766-002-0037-3

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