Bifurcation problems for superlinear elliptic indefinite equations with exponential growth

摘要

This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem $$ (P)left{ {begin{array}{*{20}l} {{ - Delta u = lambda u + h(x)phi (u)e^{u} {text{ in }}mathbb{R}^{2} }} {{u geq 0,,u to 0,{text{ when }}||x||, to + infty }} end{array} } right. $$ We consider a function h which is smooth and changes sign.