Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior

Liang, Zhanping; Li, Fuyi; Shi, Junping

Liang, Zhanping ; Li, Fuyi ; Shi, Junping

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014), p. 155-167 / Harvested from Numdam

Résumé

Existence and bifurcation of positive solutions to a Kirchhoff type equation ${\begin{matrix} - (a + b \int_{Ω} {| \nabla u |}^{2}) Δ u = ν f (x, u), & in Ω, \\ u = 0, & on \partial Ω \end{matrix}$ 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.

Publié le : 2014-01-01

MR 3165283 | Zbl 1288.35456

DOI : https://doi.org/10.1016/j.anihpc.2013.01.006

@article{AIHPC_2014__31_1_155_0,
     author = {Liang, Zhanping and Li, Fuyi and Shi, Junping},
     title = {Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {31},
     year = {2014},
     pages = {155-167},
     doi = {10.1016/j.anihpc.2013.01.006},
     mrnumber = {3165283},
     zbl = {1288.35456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2014__31_1_155_0}
}

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) pp. 155-167. doi : 10.1016/j.anihpc.2013.01.006. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_1_155_0/

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