# Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)

Archivum Mathematicum (2005)

- Volume: 041, Issue: 2, page 209-227
- ISSN: 0044-8753

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topLiu, Yuji, and Ge, Weigao. "Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)." Archivum Mathematicum 041.2 (2005): 209-227. <http://eudml.org/doc/249511>.

@article{Liu2005,

abstract = {In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equation \[ x^\{(n)\}(t)=f(t,x(t),x^\{\prime \}(t),\dots ,x^\{(n-1)\}(t))+e(t)\,,\quad 0<t<1\,,\qquad \mathrm \{\{(\ast )\}\}\]
and the following multi-point boundary value conditions \begin\{align*\}\{1\}\{*\}\{-1\} x^\{(i)\}(0)&=0\quad \mbox \{for\}\quad i=0,1,\dots ,n-3\,,\\ x^\{(n-1)\}(0)&=\alpha x^\{(n-1)\}(\xi )\,,\quad x^\{(n-2)\}(1)=\sum \_\{i=1\}^m\beta \_ix^\{(n-2)\}(\eta \_i)\,. **\end\{align*\}
Sufficient conditions for the existence of at least one solution of the BVP $(\ast )$ and $(\ast \ast )$ at resonance are established. The results obtained generalize and complement those in [13, 14]. This paper is directly motivated by Liu and Yu [J. Pure Appl. Math. 33 (4)(2002), 475–494 and Appl. Math. Comput. 136 (2003), 353–377].},

author = {Liu, Yuji, Ge, Weigao},

journal = {Archivum Mathematicum},

keywords = {solution; resonance; multi-point boundary value problem; higher order differential equation},

language = {eng},

number = {2},

pages = {209-227},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)},

url = {http://eudml.org/doc/249511},

volume = {041},

year = {2005},

}

TY - JOUR

AU - Liu, Yuji

AU - Ge, Weigao

TI - Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)

JO - Archivum Mathematicum

PY - 2005

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 041

IS - 2

SP - 209

EP - 227

AB - In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equation \[ x^{(n)}(t)=f(t,x(t),x^{\prime }(t),\dots ,x^{(n-1)}(t))+e(t)\,,\quad 0<t<1\,,\qquad \mathrm {{(\ast )}}\]
and the following multi-point boundary value conditions \begin{align*}{1}{*}{-1} x^{(i)}(0)&=0\quad \mbox {for}\quad i=0,1,\dots ,n-3\,,\\ x^{(n-1)}(0)&=\alpha x^{(n-1)}(\xi )\,,\quad x^{(n-2)}(1)=\sum _{i=1}^m\beta _ix^{(n-2)}(\eta _i)\,. **\end{align*}
Sufficient conditions for the existence of at least one solution of the BVP $(\ast )$ and $(\ast \ast )$ at resonance are established. The results obtained generalize and complement those in [13, 14]. This paper is directly motivated by Liu and Yu [J. Pure Appl. Math. 33 (4)(2002), 475–494 and Appl. Math. Comput. 136 (2003), 353–377].

LA - eng

KW - solution; resonance; multi-point boundary value problem; higher order differential equation

UR - http://eudml.org/doc/249511

ER -

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