Multiplicity Of Solutions For Two Kinds Of P-Kirchhoff Type Elliptic Problems

In this thesis,we investigate the existence and multiplicity of solutions for two kinds of p-Kirchhoff type elliptic equations via variational method and Nehari manifold.We deal with the existence and multiplicity of positive solutions for the following p-Kirchhoff type involving the critical exponent where 0? ? is a smooth bounded domain in RN,? is a positive parameter,?pu =is the usual p-Laplace operator,M(t)= a + btm and the parametersFirstly,we obtain the local minimizer of equation(A)via the Ekeland's variational principle.Secondly,when b>0 is sufficiently small,we can find mountain path structure and obtain the second positive solution of equation(A)by the mountain pass theorem.Next,we consider the existence and multiplicity of nontrivial nonnegative solu-tions for the following p-Kirchhoff equation with nonlinear boundary condition where ? C RN is a open bounded set with Lipschitz boundary(?)?,? is a positive parameter,1<s<p<r<p*,M(t)= a + btm and the parameters a,b>0,,f,g are sign-changing weight functions.We find the existence of two nontrivial nonnegative solutions of equation(B)by Nehari manifold.