Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green's Function

Habib Djourdem; Slimane Benaicha; Noureddine Bouteraa

doi:10.33434/cams.452839

EN

Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green's Function

Abstract

This paper concerns the fourth-order three-point boundary value problem (BVP) \[ u^{\left(4\right)}\left(t\right)=f\left(t,u\left(t\right)\right),\quad t\in\left[0,1\right], \] \[ u'\left(0\right)=u''\left(0\right)=u\left(1\right)=0,\;\alpha u''\left(1\right)-u'''\left(\eta\right)=0, \] where $f\in C\left(\left[0,1\right]\times\left[0,+\infty\right),\left[0,+\infty\right)\right)$, $\alpha\in\left[0,1\right)$ and $\eta\in\left[\frac{2\alpha+10}{15-2\alpha},1\right)$. Although the corresponding Green\textquoteright s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on $f$ by applying the two-fixed-point theorem due to Avery and Henderson. An example is also given to illustrate the main results.

Keywords

two positive solutions,Completely continuous,fourth-order boundary value problem,Green\textquoteright s function,two positive solutions

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Habib Djourdem
Algeria

Slimane Benaicha This is me
Algeria

Noureddine Bouteraa
Algeria

Publication Date

March 22, 2019

Submission Date

August 10, 2018

Acceptance Date

January 21, 2019

Published in Issue

Year 2019 Volume: 2 Number: 1

DOI

https://doi.org/10.33434/cams.452839

IZ

https://izlik.org/JA89KH28NR

APA

Djourdem, H., Benaicha, S., & Bouteraa, N. (2019). Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function. Communications in Advanced Mathematical Sciences, 2(1), 60-68. https://doi.org/10.33434/cams.452839

AMA

1.Djourdem H, Benaicha S, Bouteraa N. Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function. Communications in Advanced Mathematical Sciences. 2019;2(1):60-68. doi:10.33434/cams.452839

Chicago

Djourdem, Habib, Slimane Benaicha, and Noureddine Bouteraa. 2019. “Two Positive Solutions for a Fourth-Order Three-Point BVP With Sign-Changing Green’s Function”. Communications in Advanced Mathematical Sciences 2 (1): 60-68. https://doi.org/10.33434/cams.452839.

EndNote

Djourdem H, Benaicha S, Bouteraa N (March 1, 2019) Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function. Communications in Advanced Mathematical Sciences 2 1 60–68.

IEEE

[1]H. Djourdem, S. Benaicha, and N. Bouteraa, “Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function”, Communications in Advanced Mathematical Sciences, vol. 2, no. 1, pp. 60–68, Mar. 2019, doi: 10.33434/cams.452839.

ISNAD

Djourdem, Habib - Benaicha, Slimane - Bouteraa, Noureddine. “Two Positive Solutions for a Fourth-Order Three-Point BVP With Sign-Changing Green’s Function”. Communications in Advanced Mathematical Sciences 2/1 (March 1, 2019): 60-68. https://doi.org/10.33434/cams.452839.

JAMA

1.Djourdem H, Benaicha S, Bouteraa N. Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function. Communications in Advanced Mathematical Sciences. 2019;2:60–68.

MLA

Djourdem, Habib, et al. “Two Positive Solutions for a Fourth-Order Three-Point BVP With Sign-Changing Green’s Function”. Communications in Advanced Mathematical Sciences, vol. 2, no. 1, Mar. 2019, pp. 60-68, doi:10.33434/cams.452839.

Vancouver

1.Habib Djourdem, Slimane Benaicha, Noureddine Bouteraa. Two Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function. Communications in Advanced Mathematical Sciences. 2019 Mar. 1;2(1):60-8. doi:10.33434/cams.452839