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

SANKAR, R. R.; SREEDHAR, N.; Prasad, K. Venkatesh

doi:10.37193/cmi.2022.01.10

Cited by 2 publications

(2 citation statements)

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“…This is still a current topic that is very widely debated, as is proven in papers [1][2][3][4] considering the p-Laplacian where the accent falls on the applications and the importance of the models. Positive solutions for boundary value problems with p-Laplacian are obtained and discussed in [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

Meghea

2023

Axioms

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This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using the widely debated results of surjectivity or variational approaches, one may obtain or characterize weak solutions for Dirichlet or Newmann problems for these important operators. The relevance of these operators and the possibility to be involved in the modeling of an important class of real phenomena is once again revealed by their applications. The use of certain variational methods facilitates the complete solution of the problem using appropriate numerical methods and computational algorithms. Some theoretical results are involved to complete the solutions for a sequence of models issued from real phenomena drawing.

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Section: Introductionmentioning

confidence: 99%

Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

Meghea

2023

Axioms

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

Abstract: "This paper establishes the existence of positive solutions for 3n^th order differential equations with p-Laplacian operator"

Cited by 2 publications

References 24 publications

Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

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

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