Study On The Existence And Multiplicity Of Solutions To Nonlocal Problems With Singular Term

In this paper,the existence and multiplicity of solutions for a class of Kirchhoff equations with singular terms are studied by variational methods,the nonsmooth functional critical point theory,perturbation methods and some analytical techniques.Firstly,we study the following class of Kirchhoff type equations with singular terms and variable sign potentials 6,0<γ<1 and λ>0 is a real parameter.Suppose Q(x)is a continuous function onΩ,Q+(?)and Q-(?)0 and ∫Ω Q(x)dx<0.The existence of solutions to the equation is obtained by using the Mountain pass lemma and Ekeland’s variational principle.Secondly,we consider the following p-Laplacian Kirchhoff type equations with singular and logarithmic term where Ω(?) RN is a smooth bounded domain with boundary (?)Ω,a>0,b>0,4≤2p<q<p*and N>p,Δpu denotes the p-Laplacian operator defined by Δpu=div(|▽u|p-2▽u),0<γ<1 and λ>0 is a real parameter.The existence of multiple positive solutions to the equation is obtained by using the Mountain pass lemma and the critical point theory for nonsmooth functional.