Three positive solutions for p-Laplacian functional dynamic equations on time scales
In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, $$displaylines{ [ Phi _p(u^{Delta }(t))] ^{ abla}+a(t)f(u(t),u(mu (t)))=0,quad tin (0,T)_{mathbf{T}}, cr u_0(t)=varphi (t),quad tin [-r,0] _{mathbf{T}},...
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Texas State University
2007-06-01
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Online Access: | http://ejde.math.txstate.edu/Volumes/2007/95/abstr.html |
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doaj-b7c16f9dfebd476ea33eac7f7d4adb112020-11-25T00:44:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-06-0120079519Three positive solutions for p-Laplacian functional dynamic equations on time scalesDa-Bin WangIn this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, $$displaylines{ [ Phi _p(u^{Delta }(t))] ^{ abla}+a(t)f(u(t),u(mu (t)))=0,quad tin (0,T)_{mathbf{T}}, cr u_0(t)=varphi (t),quad tin [-r,0] _{mathbf{T}},\ u(0)-B_0(u^{Delta }(eta ))=0,quad u^{Delta }(T)=0,. }$$ using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result.http://ejde.math.txstate.edu/Volumes/2007/95/abstr.htmlTime scalep-Laplacian functional dynamic equationboundary value problempositive solutionfixed point |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Da-Bin Wang |
spellingShingle |
Da-Bin Wang Three positive solutions for p-Laplacian functional dynamic equations on time scales Electronic Journal of Differential Equations Time scale p-Laplacian functional dynamic equation boundary value problem positive solution fixed point |
author_facet |
Da-Bin Wang |
author_sort |
Da-Bin Wang |
title |
Three positive solutions for p-Laplacian functional dynamic equations on time scales |
title_short |
Three positive solutions for p-Laplacian functional dynamic equations on time scales |
title_full |
Three positive solutions for p-Laplacian functional dynamic equations on time scales |
title_fullStr |
Three positive solutions for p-Laplacian functional dynamic equations on time scales |
title_full_unstemmed |
Three positive solutions for p-Laplacian functional dynamic equations on time scales |
title_sort |
three positive solutions for p-laplacian functional dynamic equations on time scales |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2007-06-01 |
description |
In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, $$displaylines{ [ Phi _p(u^{Delta }(t))] ^{ abla}+a(t)f(u(t),u(mu (t)))=0,quad tin (0,T)_{mathbf{T}}, cr u_0(t)=varphi (t),quad tin [-r,0] _{mathbf{T}},\ u(0)-B_0(u^{Delta }(eta ))=0,quad u^{Delta }(T)=0,. }$$ using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result. |
topic |
Time scale p-Laplacian functional dynamic equation boundary value problem positive solution fixed point |
url |
http://ejde.math.txstate.edu/Volumes/2007/95/abstr.html |
work_keys_str_mv |
AT dabinwang threepositivesolutionsforplaplacianfunctionaldynamicequationsontimescales |
_version_ |
1725275691498340352 |