Document Type : Original Article

Authors

• Sreedhar Namburi ¹
• Kapula Rajendra Prasad ²
• Ronanki Ravi Sankar ³

¹ Department of Applied Mathematics, Institute of Science, GITAM (Deemed to be University), Visakhapatnam - 530045

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

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