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1996 Bifurcation for nonlinear elliptic boundary value problems. III.
Kazuaki Taira, Kenichiro Umezu
Adv. Differential Equations 1(4): 709-727 (1996).


This paper is devoted to global static bifurcation theory for a class of degenerateboundary value problems for nonlinear second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems. In the previous paper [13] we treated the asymptotic linear case, for example, such nonlinear terms as $u^p$, $p > 1$, near $u = 0$ but $u + 1/u$ near $u = +\infty$. The purpose of this paper is to study the asymptotic nonlinear case, for example, such nonlinear terms as $u^p$ also near $u = +\infty$. First we prove a general existence and uniqueness theorem of positive solutions for our nonlinear boundary value problems, by using the super-subsolution method, and then we study in great detail the asymptotic nonlinear case.


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Kazuaki Taira. Kenichiro Umezu. "Bifurcation for nonlinear elliptic boundary value problems. III.." Adv. Differential Equations 1 (4) 709 - 727, 1996.


Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0860.35039
MathSciNet: MR1401410

Primary: 35J25 , 35J65 , 35P30

Rights: Copyright © 1996 Khayyam Publishing, Inc.


Vol.1 • No. 4 • 1996
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