Existence and parameter dependence of positive solutions for third order differential equations with integral boundary conditions
首发时间:2020-04-08
Abstract: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.
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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带积分边界条件的三阶微分方程正解的存在性以及对参数的依赖性
摘要:我们研究了三阶微分方程$$\left \{\begin{array}{l} u^{'''}(t)+\lambda \omega(t)f(u(t))=0,\ t\in (0,1), \\ u(0)=\int_{0}^{1}g(s)u(s)ds,u^{'}(0)=u^{'}(1)=0,\end{array}\right.$$其中,$ \lambda $是一个正参数,当$1\leq p\leq +\infty $时,有$\omega \in L^{P}[0,1]$,$ g \in C[0,1]$ 是一个非负的函数。进而,通过运用特征值理论,我们得到了关于正解的新的、更一般的结果。同样我们也考虑了正解的非存在性以及正解对于参数$\lambda$的依赖性。
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带积分边界条件的三阶微分方程正解的存在性以及对参数的依赖性
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