Existence Theory For Single And Multiple Solutions To Nonlinear Singular Semi-Positone Boundary Value Problems

By using some specially constructed cones and the fixed point index theory, this paper investigates the existence of single and multiple positive solutions to some singular semipositone boundary value problems. In chapter 1, we discuss a class of second order Dirichlet boundary value problems and obtain the existence of at least one positive solution, where the nonlinearity is superlinear and may have very strong singularity. In chapter 2, we obtain the results of multiple positive solutions to the n-th order conjugate boundary value problems, but we have to add some integrability conditions to the nonlinearity. However, In chapter 3, we can also obtain multiple positive solutions without the integrability conditions above to a class of three-order three-point singular semipositone engienvalue problems. Furthermore, the corresponding nonlinearity may not have any monotonicity.