Nonsymmetric solutions of a nonlinear boundary value problem

Sámuel Peres

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 495-508
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Peres, Sámuel. "Nonsymmetric solutions of a nonlinear boundary value problem." Czechoslovak Mathematical Journal 64.2 (2014): 495-508. <http://eudml.org/doc/261998>.

@article{Peres2014,
abstract = {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.},
author = {Peres, Sámuel},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear second order ordinary differential equation; existence of solution; multiplicity of solution; nonlinear boundary condition; shooting method; time map; nonlinear second-order ordinary differential equation; existence of solutions; multiplicity of solutions; nonlinear boundary conditions; shooting method; time map},
language = {eng},
number = {2},
pages = {495-508},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonsymmetric solutions of a nonlinear boundary value problem},
url = {http://eudml.org/doc/261998},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Peres, Sámuel
TI - Nonsymmetric solutions of a nonlinear boundary value problem
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 495
EP - 508
AB - 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.
LA - eng
KW - nonlinear second order ordinary differential equation; existence of solution; multiplicity of solution; nonlinear boundary condition; shooting method; time map; nonlinear second-order ordinary differential equation; existence of solutions; multiplicity of solutions; nonlinear boundary conditions; shooting method; time map
UR - http://eudml.org/doc/261998
ER -

References

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