Existence and iteration of positive solutions for a singular two-point boundary value problem with a p -Laplacian operator

De-xiang Ma; Weigao Ge; Zhan-Ji Gui

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 135-152
  • ISSN: 0011-4642

Abstract

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In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation ( φ p ( u ' ) ) ' + q ( t ) f ( u ) = 0 , 0 < t < 1 , where φ p ( s ) : = | s | p - 2 s , p > 1 , subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient q ( t ) may be singular at t = 0 , 1 .

How to cite

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Ma, De-xiang, Ge, Weigao, and Gui, Zhan-Ji. "Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator." Czechoslovak Mathematical Journal 57.1 (2007): 135-152. <http://eudml.org/doc/31119>.

@article{Ma2007,
abstract = {In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^\{\prime \}))^\{\prime \}+q(t)f(u)=0$, $0<t<1$, where $\phi _p(s):=|s|^\{p-2\}s$, $p>1$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$.},
author = {Ma, De-xiang, Ge, Weigao, Gui, Zhan-Ji},
journal = {Czechoslovak Mathematical Journal},
keywords = {iteration; symmetric and monotone positive solution; nonlinear boundary value problem; $p$-Laplacian; iteration; symmetric and monotone positive solution; nonlinear boundary value problem; -Laplacian},
language = {eng},
number = {1},
pages = {135-152},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator},
url = {http://eudml.org/doc/31119},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Ma, De-xiang
AU - Ge, Weigao
AU - Gui, Zhan-Ji
TI - Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 135
EP - 152
AB - In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^{\prime }))^{\prime }+q(t)f(u)=0$, $0<t<1$, where $\phi _p(s):=|s|^{p-2}s$, $p>1$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$.
LA - eng
KW - iteration; symmetric and monotone positive solution; nonlinear boundary value problem; $p$-Laplacian; iteration; symmetric and monotone positive solution; nonlinear boundary value problem; -Laplacian
UR - http://eudml.org/doc/31119
ER -

References

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  5. 10.1016/S0898-1221(01)00188-2, Comput. Math. Appl. 42 (2001), 695–704. (2001) MR1838025DOI10.1016/S0898-1221(01)00188-2
  6. 10.1006/jmaa.2001.7742, J.  Math. Anal. Appl. 266 (2002), 383–340. (2002) MR1880513DOI10.1006/jmaa.2001.7742
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  8. 10.1137/1018114, SIAM Rev. 18 (1976), 620–709. (1976) MR0415432DOI10.1137/1018114

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