变系数四阶边值问题正解存在性

该文结合算子谱论,应用锥不动点定理,建立了四阶边值问题\\left\{ {\begin{array}{l}u^{(4)} + B(t){u}' - A(t)u = f(t,u),0 < t < 1 ,\\u(0) = u(1) = {u}'(0) = {u}'(1) = 0 \end{array}} \right.\]正解存在性定理,这里$A(t),B(t) \in C0,1]$,$f(t,u):0,1]\times0,\infty ) \to 0,\infty )$连续.

Existence of Positive Solutions for Fourth-Order Boundary Value Problem with Variable Coefficients

In this paper, by use of the fixed pointtheorem, combining spectral theory of operator, the authorsestablish the theorem on existence of positive solutions forfourth-order boundary value problem with variable coefficient asfollows\\left\{ {\begin{array}{l} u^{(4)} + B(t){u}' - A(t)u = f(t,u),0 < t < 1 ,\\ u(0) = u(1) = {u}'(0) = {u}'(1) = 0 \end{array}} \right.\]\noindent where $A(t),B(t) \in C0,1]$ and $f(t,u):0,1]\times 0,\infty ) \to0,\infty )$ is continuous.