Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line
This paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\ x(0)=\sum\limits_{i=1}^{n}\mu_ix(\xi_{i}),...
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University of Szeged
2009-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=371 |
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doaj-0c16bc82311b47e5b2c79393e724cba52021-07-14T07:21:20ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752009-03-0120091911510.14232/ejqtde.2009.1.19371Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-lineAijun Yang0Chunmei Miao1Weigao Ge2Department of Mathematics, Zhejiang University of TechnologyCollege of Science, Changchun University, Changchun, P. R. ChinaBeijing Institute of Technology, Beijing, P. R. ChinaThis paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\ x(0)=\sum\limits_{i=1}^{n}\mu_ix(\xi_{i}), ~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right.$$ and $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'+g(t)h(t,x(t),x'(t))=0,~~~~0<t<\infty,\\ x(0)=\int_{0}^{\infty}g(s)x(s)ds,~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right. $$ with multi-point and integral boundary conditions, respectively, where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. The arguments are based upon an extension of Mawhin's continuation theorem due to Ge. And examples are given to illustrate our results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=371 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Aijun Yang Chunmei Miao Weigao Ge |
| spellingShingle |
Aijun Yang Chunmei Miao Weigao Ge Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line Electronic Journal of Qualitative Theory of Differential Equations |
| author_facet |
Aijun Yang Chunmei Miao Weigao Ge |
| author_sort |
Aijun Yang |
| title |
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line |
| title_short |
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line |
| title_full |
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line |
| title_fullStr |
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line |
| title_full_unstemmed |
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line |
| title_sort |
solvability for second-order nonlocal boundary value problems with a p-laplacian at resonance on a half-line |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
2009-03-01 |
| description |
This paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line
$$\left\{\begin{array}{llll}
(c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\
x(0)=\sum\limits_{i=1}^{n}\mu_ix(\xi_{i}),
~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0
\end{array}\right.$$
and
$$\left\{\begin{array}{llll}
(c(t)\phi_{p}(x'(t)))'+g(t)h(t,x(t),x'(t))=0,~~~~0<t<\infty,\\
x(0)=\int_{0}^{\infty}g(s)x(s)ds,~~\lim\limits_{t\rightarrow
+\infty}c(t)\phi_{p}(x'(t))=0
\end{array}\right.
$$
with multi-point and integral boundary conditions, respectively, where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. The arguments are based upon an extension of Mawhin's continuation theorem due to Ge. And examples are given to illustrate our results. |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=371 |
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AT aijunyang solvabilityforsecondordernonlocalboundaryvalueproblemswithaplaplacianatresonanceonahalfline AT chunmeimiao solvabilityforsecondordernonlocalboundaryvalueproblemswithaplaplacianatresonanceonahalfline AT weigaoge solvabilityforsecondordernonlocalboundaryvalueproblemswithaplaplacianatresonanceonahalfline |
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