Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension p -Laplacian

Daqing Jiang; Li Li Zhang; Donal O'Regan; Ravi P. Agarwal

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 367-381
  • ISSN: 0044-8753

Abstract

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In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem Δ [ φ ( Δ u ( t - 1 ) ) ] + q ( t ) f ( t , u ( t ) ) = 0 , t ∈ { 1 , 2 , ⋯ , T } u ( 0 ) = u ( T + 1 ) = 0 , where φ ( s ) = | s | p - 2 s , p > 1 and our nonlinear term f ( t , u ) may be singular at u = 0 .

How to cite

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Jiang, Daqing, et al. "Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$-Laplacian." Archivum Mathematicum 040.4 (2004): 367-381. <http://eudml.org/doc/249291>.

@article{Jiang2004,
abstract = {In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem \[ \left\lbrace \begin\{array\}\{l\} \Delta \big [\phi (\Delta u(t-1))\big ]+ q(t) f(t,u(t))=0\,,\quad t\in \lbrace 1,2,\dots ,T\rbrace \\[3pt] u(0)=u(T+1)=0\,, \end\{array\} \right. \] where $\phi (s) = |s|^\{p-2\}s$, $p>1$ and our nonlinear term $f(t,u)$ may be singular at $u=0$.},
author = {Jiang, Daqing, Zhang, Li Li, O'Regan, Donal, Agarwal, Ravi P.},
journal = {Archivum Mathematicum},
keywords = {multiple solutions; singular; existence; discrete boundary value problem; discrete Dirichlet boundary value problem; one-dimensional -Laplacian; positive solution; Leray-Schauder alternative; cone fixed point theorem},
language = {eng},
number = {4},
pages = {367-381},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$-Laplacian},
url = {http://eudml.org/doc/249291},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Jiang, Daqing
AU - Zhang, Li Li
AU - O'Regan, Donal
AU - Agarwal, Ravi P.
TI - Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension $p$-Laplacian
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 367
EP - 381
AB - In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem \[ \left\lbrace \begin{array}{l} \Delta \big [\phi (\Delta u(t-1))\big ]+ q(t) f(t,u(t))=0\,,\quad t\in \lbrace 1,2,\dots ,T\rbrace \\[3pt] u(0)=u(T+1)=0\,, \end{array} \right. \] where $\phi (s) = |s|^{p-2}s$, $p>1$ and our nonlinear term $f(t,u)$ may be singular at $u=0$.
LA - eng
KW - multiple solutions; singular; existence; discrete boundary value problem; discrete Dirichlet boundary value problem; one-dimensional -Laplacian; positive solution; Leray-Schauder alternative; cone fixed point theorem
UR - http://eudml.org/doc/249291
ER -

References

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