Existence of Positive Solutions for 2n-Order Lidstone Boundary Value Problems with P-Laplacian Operator

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  • Sreedhar Namburi1,
  • Kapula Rajendra Prasad2,
  • Ronanki Ravi Sankar3,
  1. Department of Applied Mathematics, Institute of Science, GITAM (Deemed to be University), Visakhapatnam -
  2. Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530 003, India
  3. Department of Mathematics, Government Degree College, Tekkali, Srikakulam, 532 201, India

Published in Issue 2025-11-09

How to Cite

Existence of Positive Solutions for 2n-Order Lidstone Boundary Value Problems with P-Laplacian Operator. (2025). Communications in Nonlinear Analysis, 10(2). https://oiccpress.com/cna/article/view/17846

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Abstract

In this paper, we establish the existence of positive solutions for $2n^{text {th}}$ order Lidstone boundary value problems with $p$-Laplacian of the form$$(-1)^n[phi_{p}(y^{(2n-2)}(t)-k^2y^{(2n-4)}(t))]''=f(t,y(t)), ~~t in [0, 1], $$$$y^{(2i)}(0)=0=y^{(2i)}(1), for $0leq i leq n-1,$ where $ngeq 2$ and $k>0$ is a constant, by applying Guo--Krasnosel'skii fixed point theorem.

Keywords

  • Green’s function,
  • p-Laplacian,
  • boundary value problem,
  • positive solution,
  • cone,
  • fixed point theorem
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