Existence of Positive Solutions for Higher Order p-Laplacian Boundary Value Problems

Prasad, K. Venkatesh; Sreedhar, N.; Wesen, L. T.

doi:10.1007/s00009-017-1064-x

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…By taking n = 1 and p = 2 in (1.1) and (1.2), reduces to third order three-point boundary value problem and studied the existence of positive solutions based on various methods by many researchers, see [7,13,14,15,16,18,19,27,29,31]. However, as per our knowledge, very few works have been found in the literature on the existence of positive solutions of higher order boundary value problems with p-Laplacian, see [5,21,25,26,30]. Motivated by above papers, we extend the results to the problem (1.1)-(1.2).…”

Section: Introductionmentioning

confidence: 99%

"Existence of positive solutions for 3n^th order boundary value problems involving p-Laplacian"

SANKAR¹,

SREEDHAR²,

Prasad³

2022

CMI

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Section: Introductionmentioning

confidence: 99%

"Existence of positive solutions for 3n^th order boundary value problems involving p-Laplacian"

SANKAR¹,

SREEDHAR²,

Prasad³

2022

CMI

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“…If p = 2, we get various order three-point boundary value problems by giving different values to m and n. In the past, most researchers have focussed and demonstrated the positivity results for boundary value problems of third order three-point using various methods, see [11,29,33,35,22,23,25,27,34,24,39]. However, some works on positivity results have been found for n th , 2n th and 3n th order p-Laplacian boundary value problems, see [21,12,32,38,8,36,37,30,31]. Motivated by the aforementioned papers, we then extend the results to mn th order p-Laplacian problem stated in (1), (2).…”

Section: Introductionmentioning

confidence: 99%

Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian

SANKAR

Sreedhar

Prasad

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving $p$-Laplacian $$[\phi_{p}(x^{(m)}(t))]^{(n)}=g(t,x(t)),~~t \in [0, 1],$$ $$ \begin{aligned} x^{(i)}(0)=0, &\text{~for~} 0\leq i\leq m-2,\\ x^{(m-2)}(1)&-\alpha x^{(m-2)}(\xi)=0,\\ [\phi_{p}(x^{(m)}(t))]^{(j)}_{\text {at} ~ t=0}&=0, \text{~for~} 0\leq j\leq n-2,\\ [\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=1}&-\alpha[\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=\xi}=0, \end{aligned} $$ where $m,n\geq 3$, $\xi\in(0,1)$, $\alpha\in (0,\frac{1}{\xi})$ is a parameter. The approach used by the application of Guo--Krasnosel'skii fixed point theorem to determine the existence of positivity of the solutions to the problem.

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“…In particular, for more results on the asymptotic behaviors of third‐order delay or neutral differential equations, see the books of Berezansky et al, 5 Burton, 6 and Smart 7 as a good survey for the works and the papers of Ardjouni and Rezaiguia, 8 Ardjouni and Djoudi, 9 Cheng and Ren, 10 Cheng and Xin, 11 Li, 1 Nieto, 12 Lv and Cheng, 13 Prasad et al, 14 Zang, 15 Padhi and Pati, 16 Tunç, 17 Omeike, 18 Zhu, 19 Ademola and Arawomo, 20 Domoshnitsky et al, 21 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Lemma (Prasad et al 14 ). If