【摘要】 研究了非线性2阶Dirichlet边值问题u″(t)-λu(t)+h(t)f(t,u(t))+g(t,u(t))=0 0<t<1,u(0)=u(1)=0的正解存在性与多解性,其中λ>-π2是常数,而g(t,u)可以在u=0处奇异.通过精确估计解的先验界并且利用锥拉伸-压缩的Guo-Krasnoselskii不动点定理,建立了几个存在定理.更多还原

【Abstract】 The existence and multiplicity of positive solutions are studied for the nonlinear second-order Dirichlet boundary value problem u″(t)-λu(t) +h(t)f(t,u(t))+g(t,u(t))=0 0<t<1,u(0) =u(1) =0,where λ>-π2 is a constant and g(t,u) may be singular at u=0.By exactly estimating the priori bound of solution and applying the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type,several existence theorems are established.更多还原