Existence Of Bound State Solutions And Positive Solutions For Kirchhoff-Type Equations With Concave Terms

This paper investigates the existence of bound state solutions and positive solutions for Kirchhoff-type equations.Firstly,we consider the following Kirchhoff-type problem with concave-convex nonlinearities:where a,b>0 are two constants,1<q<2,4<p<6,f∈L2/(2-q)(R3)is a negative function.Under some appropriate assumptions on f,problem(0.0.3)has a bound state solution by using a linking theorem and Nehari manifold.Next,we consider the following Kirchhoff-type problem with concave nonlinear terms:where a,b>0,1<q<2,Ω is a bounded domain with a C2-boundary ?Ω in RN(N=1,2,3).If f is a Caratheodory function and satisfies some conditions,by applying variational methods,there exists a constant λ*>0 such that for any λ∈(0,λ*),problem(0.0.4)has at least two positive solutions.