Multiple positive solutions for a class of variational systems

Authors

A Castro, Harvey Mudd College
D Costa, University of Nevada, Las Vegas
R Shivaji, University of North Carolina at Greensboro

Document Type

Article

Publication Date

1-1-2017

Publication Title

Topological Methods in Nonlinear Analysis

Volume

50

Issue

1

First page number:

1

Last page number:

8

Abstract

We consider the variational system −∆u = λ(∇F)(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded region in ℝm (m ≥ 1) with C1 boundary, λ is a positive parameter, u: Ω → ℝN (N > 1), and ∆ denotes the Laplace operator. Here F: ℝN → ℝ is a function of class C2. Using variational methods, we show how changes in the sign of F lead to multiple positive solutions. © 2017 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University.

File Format

pdf

File Size

295.83 KB

Language

english

Repository Citation

Castro, A., Costa, D., Shivaji, R. (2017). Multiple positive solutions for a class of variational systems. Topological Methods in Nonlinear Analysis, 50(1), 1-8.
http://dx.doi.org/10.12775/TMNA.2017.016