## Abstract and Applied Analysis

### Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems

#### Abstract

We are concerned with determining values of $\lambda$, for which there exist positive solutions of the nonlinear elliptic problem $-\mathrm{\Delta }u=\lambda a(x)f(u) \text{in}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\mathrm{\Omega }$, $\partial u/\partial \mathbf{n}+b(x)g(u)=\mathrm{0}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\text{on}\text{\hspace\{0.17em\}}\text{\hspace\{0.17em\}}\partial \mathrm{\Omega }.$ The proof of our main results is based upon unilateral global bifurcation theorem of López-Gómez.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 749368, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277015

Digital Object Identifier
doi:10.1155/2014/749368

Mathematical Reviews number (MathSciNet)
MR3216072

Zentralblatt MATH identifier
07023014

#### Citation

Ma, Ruyun; Lu, Yanqiong; Chen, Ruipeng. Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems. Abstr. Appl. Anal. 2014 (2014), Article ID 749368, 7 pages. doi:10.1155/2014/749368. https://projecteuclid.org/euclid.aaa/1412277015

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