Existence And Multiplicity Of Solutions For Some Nonlocal Boundary Value Problems

In this thesis, by using the Rabinowitz’s global bifurcation theorem, we study the existence of sign-changing and positive solutions of second-order differential equations with linear and nonlinear integral boundary conditions, respectively. We describe them in detail as follows.1. we study the existence and global structure of sign-changing solutions for second-order differential equations with linear integral boundary conditions where λ>0 is a parameter, A:[0,1]→R+ is nondecreasing and A（t） is not a constant on （0,1）, and （?） dA（t）∈ [0,1);f∈C¹ （R, R） satisfies sf（s）>0 for s≠ 0; the limits f₀:=（?）f（s）/s=0,f_∞:=（?） f（s）/s=0.The main results extend and improve the corresponding ones of Yulian An [Math. Anal.,2012] and Ruyun Ma [Nonlinear Anal,2009].2. By using Rabinowitz’s global bifurcation theorem, the Topological degree theory, we study the existence of positive solutions for second-order differential e-quations with nonlinear integral boundary conditions where λ> 0 is a parameter, A:[0,1]→R is nondecreasing and A（t） is not a constant on （0,1）, K（s）:=（?） k（t, s）dA（t）≥0 for s ∈[0,1], and Γ:= f₀¹ tdA（t） ∈ [0,1);f∈ C[0,1);F∈c（[0,1]×[0,∞）,[0,∞)),G∈C（[0,∞）,[0,∞)), f（t, s） and g（s） are not necessarily linearizable near s=0 and infinity. The main results improve the corresponding ones of Ruyun Ma [Nonlinear Anal.,2009] and Webb [Nonlinear Differential Equations Appl.,2008].