Multi-point Boundary Value Problems For Second-order Differential Equations

In this thesis of master, we maily investigate the existence of solutions to multi-point boundary value problems for second-order differential equations. It is consists of three chapters.In chapter 1, we discuss the existence of positive solutions to three-point boundary value problems for second-order singular differential equationswhere f∈C((0,+∞), (0,+∞)) and f(x) at x = 0, q(t) at t = 0 or 1 may have singularity,λ> 0 is parameter, 0 <α,β,η< 1 are constants and 0<α+β< 1.In chapter 2, we discuss the existence of extreme solutions to multi-point boundary value problems for second-order integro-differential equationswhere J = [0,1], f∈C(J×R²,R), k(t,s)∈C{J×J, R) and k(t,s)≥0, 0≤(?) a_i≤1, a_i≥0, 0 <η_i < 1.In chapter 3, we discuss the existence of positive solutions to multi-point boundary value problems for second-order singular impulsive differential equationswhere f∈C((0, +∞), [0, +∞)), 0 = t₀ < t₁ < t₂ < ... < t_k < t_k+1 = 1,â–³x'(t_k) = x'(t_k⁺) - x'(t_k^-), 0 i,η_i < 1(i = 1,2,...,l), q(t) may have singularity at t = 0 or 1,λis positive parameter.