Multiple Sign-Changing Solutions for Kirchhoff-Type Equations

Xingping Li, Xiumei He
2015 Discrete Dynamics in Nature and Society  
We study the following Kirchhoff-type equations-a+b∫Ω∇u2dxΔu+Vxu=fx,u, inΩ,u=0, in∂Ω, whereΩis a bounded smooth domain ofRN (N=1,2,3),a>0,b≥0,f∈C(Ω¯×R,R), andV∈C(Ω¯,R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, iffis odd with respect to its second variable, this problem has infinitely many sign-changing solutions.
doi:10.1155/2015/985986 fatcat:lnajyvsjszcwrdarwtaidz3yrq