Positive solutions of a fourth-order differential equation with integral boundary conditions

Seshadev Padhi; John R. Graef

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 4, page 583-601
  • ISSN: 0862-7959

Abstract

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We study the existence of positive solutions to the fourth-order two-point boundary value problem where is a Riemann-Stieltjes integral with being a nondecreasing function of bounded variation and . The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii’s fixed point theorem and the Avery-Peterson fixed point theorem.

How to cite

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Padhi, Seshadev, and Graef, John R.. "Positive solutions of a fourth-order differential equation with integral boundary conditions." Mathematica Bohemica 148.4 (2023): 583-601. <http://eudml.org/doc/299359>.

@article{Padhi2023,
abstract = {We study the existence of positive solutions to the fourth-order two-point boundary value problem \[ \{\left\lbrace \begin\{array\}\{ll\} u^\{\prime \prime \prime \prime \}(t) + f(t,u(t))=0, & 0 < t < 1,\\ u^\{\prime \}(0) = u^\prime (1) = u^\{\prime \prime \}(0) =0, & u(0) = \alpha [u], \end\{array\}\right.\} \] where $\alpha [u]=\int ^\{1\}_\{0\}u(t)\{\rm d\}A(t)$ is a Riemann-Stieltjes integral with $A \ge 0$ being a nondecreasing function of bounded variation and $f \in \mathcal \{C\}([0,1] \times \mathbb \{R\}_\{+\}, \mathbb \{R\}_\{+\})$. The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii’s fixed point theorem and the Avery-Peterson fixed point theorem.},
author = {Padhi, Seshadev, Graef, John R.},
journal = {Mathematica Bohemica},
keywords = {boundary value problem; fixed point; positive solution; cone; existence theorem},
language = {eng},
number = {4},
pages = {583-601},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive solutions of a fourth-order differential equation with integral boundary conditions},
url = {http://eudml.org/doc/299359},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Padhi, Seshadev
AU - Graef, John R.
TI - Positive solutions of a fourth-order differential equation with integral boundary conditions
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 583
EP - 601
AB - We study the existence of positive solutions to the fourth-order two-point boundary value problem \[ {\left\lbrace \begin{array}{ll} u^{\prime \prime \prime \prime }(t) + f(t,u(t))=0, & 0 < t < 1,\\ u^{\prime }(0) = u^\prime (1) = u^{\prime \prime }(0) =0, & u(0) = \alpha [u], \end{array}\right.} \] where $\alpha [u]=\int ^{1}_{0}u(t){\rm d}A(t)$ is a Riemann-Stieltjes integral with $A \ge 0$ being a nondecreasing function of bounded variation and $f \in \mathcal {C}([0,1] \times \mathbb {R}_{+}, \mathbb {R}_{+})$. The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii’s fixed point theorem and the Avery-Peterson fixed point theorem.
LA - eng
KW - boundary value problem; fixed point; positive solution; cone; existence theorem
UR - http://eudml.org/doc/299359
ER -

References

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