Existence of Multiple Solutions of Boundary Value Problems for a Class of Kirchhoff-Type Equation
In this paper,we consider the existence of multiple solutions of boundary value problems for a Kirchhoff-type equation{-(a+b ‖u ‖2)Δu=bμu3+f(x,u),x∈Ωu=0,x∈∂Ωwhere Ω⊂RN is a bounded smooth domain(N=1,2,3)and a,b＞0,μ ∈ R is a parame-ter.μ is less than the principal eigenvalue of Nonlinear eigenvalue problem:｛-‖u∫Δu=μu3,x∈Ω,u-0,x∈∂Ωthat is μ＜µ1.F(x,t)=∫10(x,s)ds,F(x,u)∈C1(Ω×R,R)satisfies 4-sublinear at infinity.We proved the existence of multiple pairs of solutions for Kirchhoff-type equation above by using crit-ical point theory and Clark theorem.
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