Two-Point Boundary Value Problems for a Class of Second-Order Ordinary Differential Equations

Indranil SenGupta and Maria C. Mariani

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-13

Abstract:

We study the general semilinear second-order ODE ð ‘¢ î…ž î…ž + ð ‘” ( ð ‘¡ , ð ‘¢ , ð ‘¢ î…ž ) = 0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on ð ‘” , we prove that the set of solutions of ð ‘¢ î…ž î…ž + ð ‘” ( ð ‘¡ , ð ‘¢ , ð ‘¢ î…ž ) = 0 is homeomorphic to the two-dimensional real space.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:794040

DOI: 10.1155/2012/794040

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