Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior
نویسندگان
چکیده
Existence and bifurcation of positive solutions to a Kirchhoff type equation ⎧⎪⎨ ⎪⎩ − ( a + b ∫ Ω |∇u|2 ) u= νf (x,u), in Ω, u= 0, on ∂Ω 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. © 2013 Elsevier Masson SAS. All rights reserved.
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