Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 293-300.

Existence and multiplicity results for p-q-Laplacian boundary value problems

Ananta Acharya, Ujjal Das, Ratnasingham Shivaji

Abstract:
We study positive solutions to the boundary value problem

where $q \in (1,p)$ and Ω is a bounded domain in $\mathbb{R}^N$, N >1 with smooth boundary, λ is a positive parameter, and $f:[0,\infty) \to (0,\infty)$ is C1, nondecreasing, and p-sublinear at infinity i.e. $\lim_{t \to \infty} f(t)/t^{p-1}=0$. We discuss existence and multiplicity results for classes of such f. Further, when N=1, we discuss an example which exhibits S-shaped bifurcation curves.

Published January 18, 2022.
Math Subject Classifications: 35J70, 35J55.
Key Words: Multiple positive solutions; p-q Laplacian; sub-super solution.

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Ananta Acharya
Department of Mathematics and Statistics
University of North Carolina at Greensboro
Greensboro, NC 27412, USA
email: a_achary@uncg.edu
Ujjal Das
Technion-Israel Institute of Technology
Haifa-32000, Israel
email: ujjaldas@campus.technion.ac.il, ujjal.rupam.das@gmail.com
Ratnasingham Shivaji
Department of Mathematics and Statistics
University of North Carolina at Greensboro
Greensboro, NC 27412, USA
email: r_shivaj@uncg.edu

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