【摘要】 研究非线性三阶微分方程x’’’=f(t,x,x’,x″),t∈[0,1],分别满足三点边界条件x(0)=0,ax’(0)-bx″(0)=0,x’(1)=αx’(ξ)和x’(0)=βx’(η),x(1)=0,cx’(1)+dx″(1)=0的两类边值问题解的存在性.利用Leray-Schauder度理论,给出上述两类三阶三点边值问题解的存在性的若干充分条件.更多还原

【Abstract】 We investigate the existence of solutions for nonlinear third-order differential equarions x’’’= f( t,x,x’,x″),t∈[0,1]subject to the following two sets of three-point boundary problem conditions: x( 0) = 0,ax’( 0)-bx″( 0) = 0,x’( 1) = αx’( ξ) and x’( 0) = βx’( η),x( 1) = 0,cx’( 1) + dx″( 1) = 0. By using the LeraySchauder degree theory,the existence of solutions for the above boundary value problems are given.更多还原