Studies on a multi-point boundary value problem for second order differential equation with <Emphasis Type="Italic">p</Emphasis>-Laplacian |
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| Authors: | Xingyuan Liu Yuji Liu |
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| Institution: | 1.Department of Mathematics,Shaoyang University,Shaoyang,P. R. China;2.Department of Mathematics,Guangdong University of Business Studies,Guangzhou,P. R. China |
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| Abstract: | The existence of at least one solution of the following multi-point boundary value problem
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$
\left\{ \begin{gathered}
\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
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| Keywords: | |
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