Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p -Laplacian

Yūki Naito

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 2, page 175-184
  • ISSN: 0862-7959

Abstract

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We consider the boundary value problem involving the one dimensional p -Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

How to cite

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Naito, Yūki. "Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional $p$-Laplacian." Mathematica Bohemica 136.2 (2011): 175-184. <http://eudml.org/doc/197253>.

@article{Naito2011,
abstract = {We consider the boundary value problem involving the one dimensional $p$-Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.},
author = {Naito, Yūki},
journal = {Mathematica Bohemica},
keywords = {boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation; boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation},
language = {eng},
number = {2},
pages = {175-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional $p$-Laplacian},
url = {http://eudml.org/doc/197253},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Naito, Yūki
TI - Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional $p$-Laplacian
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 2
SP - 175
EP - 184
AB - We consider the boundary value problem involving the one dimensional $p$-Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
LA - eng
KW - boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation; boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation
UR - http://eudml.org/doc/197253
ER -

References

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