三阶p-Laplacian共振多点边值问题解的存在性  

Existence of Solutions of Third-Order p-Laplacian Resonant Multi-Point Boundary Value Problems

作　　者：李翠哲[1] 李志艳[1] 

机构地区：[1]北京理工大学理学院,北京100081

出　　处：《北京理工大学学报》2004年第11期1024-1029,共6页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(10371006)

摘　　要：研究了一类具有p-Laplacian算子的三阶常微分方程共振多点边值问题。通过将方程两边同时积分一次,得到等价积分方程,定义线性算子L,利用Mawhin连续定理证明积分方程在函数f(t,u,p)允许取负值时至少存在一个解,从而得到共振条件下三阶p-Laplacian算子多点边值问题解的存在性。A class of third-order ordinary differential equation resonant multi-piont boundary value problem with p-Laplacian operator is studied. By integrating on both sides of the equation once, its equivalent integral equation is obtained. By defining the linear operator L and using the Mawhin continuation theorem, it is shown that the integral equation has at least one solution when f(t,u,p) is allowed to be negative. The existence of the solution of the third-order resonant multi-piont boundary value problem with p-Laplacian operator is thus proved.

关 键 词：Mawhin连续定理 P-LAPLACIAN算子 多点边值问题 共振 

分 类 号：O175.8[理学—数学]