Multiple Solutions For Nonlinear Equations Related To Kirchhoff Type Equations

In this paper,we will use perturbation method discuss the following kirchhoff equa.tion where:,a,,b a.re positive constants,1<P<5,g(x)∈ L∞(R3).The kirchhoff type equat.ions have grea.t application in many fields,such as non-newt.oniain mecha.nics,plasma problems,and elasticity theory.Therefore,the study of this kind of problems not only has certain application value,but also has certain theoretical significance of nmathema.tics.When g(x)satisfies some conditions,we use perturbation method to prove t.hat there exists a ε0,for all ε and 0<ε<ε0,such that there are multiple solutions to the above problem.