Open Access
Translator Disclaimer
2015 The spectrum in $R$ and $R^2$ of nonlinear elliptic equations with positive parameters
Imelda Trejo, Raúl Felipe
Rocky Mountain J. Math. 45(4): 1311-1331 (2015). DOI: 10.1216/RMJ-2015-45-4-1311

Abstract

In this paper we study the spectrum in $\R$ and $\R^2$ of nonlinear elliptic equations with positive parameters in their nonlinear part. In order to investigate the spectrum in these specific cases, we introduce the monotone method which is an extension of the upper and lower solution methods. Using the Picard iterative process we prove some existence theorems for nonlinear elliptic boundary value problems. We work with both positive and negative solutions.

Citation

Download Citation

Imelda Trejo. Raúl Felipe. "The spectrum in $R$ and $R^2$ of nonlinear elliptic equations with positive parameters." Rocky Mountain J. Math. 45 (4) 1311 - 1331, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1311

Information

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 1336.35263
MathSciNet: MR3418196
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1311

Subjects:
Primary: 34B15 , 35J60

Keywords: Monotone solutions , Picard iterative process , spectrum

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.45 • No. 4 • 2015
Back to Top