Nontrivial Solutions Of Nonlinear Semipositive (k, N-k) Conjuate Boundary Value Problems

Recently, the existence of nontrivial solutions of nonlinear differential equations attracts close attention, in which the nonlinear function is endowed with the conditions of some different kinds in much literature, the eigenvalue and the spectral radius of linear completely continuous operators are very important and significant indexes. In this thesis, the eigenvalue criteria is given to the nonlinear function for the existence of nontrivial solutions and symmetric solutions of nonlinear semipositive(k,n-k)conjuate boundary value problems.In chapter 2, the nonlinear semipositive(k, n-k)conjugate boundary value problems (-1)n-kφ(n)(x)=h(x)f(φ(x)),0