On a singular multi-point third-order boundary value problem on the half-line

Zakia Benbaziz; Smail Djebali

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 3, page 305-324
  • ISSN: 0862-7959

Abstract

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We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f ( t , x , y ) which satisfies upper and lower-homogeneity conditions in the space variables x , y may be also singular at time t = 0 . Two examples of applications are included to illustrate the existence theorems.

How to cite

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Benbaziz, Zakia, and Djebali, Smail. "On a singular multi-point third-order boundary value problem on the half-line." Mathematica Bohemica 145.3 (2020): 305-324. <http://eudml.org/doc/297034>.

@article{Benbaziz2020,
abstract = {We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity $f=f(t,x,y)$ which satisfies upper and lower-homogeneity conditions in the space variables $x, y$ may be also singular at time $t=0$. Two examples of applications are included to illustrate the existence theorems.},
author = {Benbaziz, Zakia, Djebali, Smail},
journal = {Mathematica Bohemica},
keywords = {singular nonlinear boundary value problem; positive solution; Krasnosel'skii fixed point theorem; multi-point; half-line},
language = {eng},
number = {3},
pages = {305-324},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a singular multi-point third-order boundary value problem on the half-line},
url = {http://eudml.org/doc/297034},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Benbaziz, Zakia
AU - Djebali, Smail
TI - On a singular multi-point third-order boundary value problem on the half-line
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 3
SP - 305
EP - 324
AB - We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity $f=f(t,x,y)$ which satisfies upper and lower-homogeneity conditions in the space variables $x, y$ may be also singular at time $t=0$. Two examples of applications are included to illustrate the existence theorems.
LA - eng
KW - singular nonlinear boundary value problem; positive solution; Krasnosel'skii fixed point theorem; multi-point; half-line
UR - http://eudml.org/doc/297034
ER -

References

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