An application of Schauder’s fixed point theorem with respect to higher order BVPs
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Abstract:
We shall provide conditions on the function $f(t,u_{1},\cdots , u_{n-1})$. The higher order boundary value problem \begin{equation*}\begin {cases}(E)~~ u^{(n)}(t)+ f(t, u(t),u^{(1)}(t),\cdots ,u^{(n-2)}(t))=0~~~~~\mathrm {~for~}~~~~~t\in (0,1)~~~~\mathrm {and}~~~~~~n\ge 2,\ (BC)~~ \begin {cases}u^{(i)}(0)=0,~~~~~0\le i \le n-3,\ \alpha u^{(n-2)}(0)-\beta u^{(n-1)}(0)=0,\ \gamma u^{(n-2)}(1)+\delta u^{(n-1)}(1)=0\end{cases} \end{cases} \tag {{BVP}}\end{equation*} has at least one solution.References
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Additional Information
- Fu-Hsiang Wong
- Affiliation: Department of Mathematics and Science, National Taipei Teacher’s College, 134, Ho-Ping E. Rd. Sec. 2, Taipei 10659, Taiwan, Republic of China
- Email: wong@tea.ntptc.edu.tw
- Received by editor(s): January 22, 1997
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2389-2397
- MSC (1991): Primary 34B15
- DOI: https://doi.org/10.1090/S0002-9939-98-04709-1
- MathSciNet review: 1476399