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| We consider the third-order differential equations:$$\left \{\begin{array}{l} u^{'''}(t)+\lambda \omega(t)f(u(t))=0,\ t\in (0,1), \\ u(0)=\int_{0}^{1}g(s)u(s)ds,u^{'}(0)=u^{'}(1)=0,\end{array}\right.$$where $ \lambda $ is a positive parameter, $\omega \in L^{P}[0,1]$ for some $1\leq p\leq +\infty $, and $ g \in C[0,1]$ is a nonnegative function. Furthermore, some new and more general results are presented on the existence of positive solutions for the above problem by using the eigenvalue theory. Nonexistence results and the dependence of positive solutions on the parameter $\lambda$ are also considered. |
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| Keywords:Green's function; Third order differential equations; Eigenvalue theory; Integral boundary conditions; Existence and nonexistence; Parameter dependence of positive solution |
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