Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 155-167.

Existence and bifurcation of positive solutions to a Kirchhoff type equation

{-(a+b Ω|u| 2 )Δu=νf(x,u),inΩ,u=0,onΩ
are considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff type equation in bounded domain, and in our results the nonlinearity may be resonant near zero or infinity.

DOI : 10.1016/j.anihpc.2013.01.006
Mots clés : Kirchhoff type equation, Topological degree, Variational method, Monotone operator, Bifurcation
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     title = {Positive solutions to {Kirchhoff} type equations with nonlinearity having prescribed asymptotic behavior},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {155--167},
     publisher = {Elsevier},
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Liang, Zhanping; Li, Fuyi; Shi, Junping. Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 155-167. doi : 10.1016/j.anihpc.2013.01.006. http://www.numdam.org/articles/10.1016/j.anihpc.2013.01.006/

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