Geodesic
Nonsymmetric solutions of a nonlinear boundary value problem
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 495-508 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study the existence and multiplicity of positive nonsymmetric and sign-changing nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing open question whether or not these conditions can be omitted. In this article we provide the answer. Our main tool is the shooting method.
We study the existence and multiplicity of positive nonsymmetric and sign-changing nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing open question whether or not these conditions can be omitted. In this article we provide the answer. Our main tool is the shooting method.
DOI : 10.1007/s10587-014-0115-8
Classification : 34B08, 34B15, 34B18
Keywords: nonlinear second order ordinary differential equation; existence of solution; multiplicity of solution; nonlinear boundary condition; shooting method; time map 
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Peres, Sámuel. Nonsymmetric solutions of a nonlinear boundary value problem. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 495-508. doi: 10.1007/s10587-014-0115-8

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