Positive Solutions for Third-Order Nonlinearp-Laplacianm-Point Boundary Value Problems on Time Scales
2008 ◽
Vol 2008
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pp. 1-16
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Keyword(s):
We study the following third-orderp-Laplacianm-point boundary value problems on time scales:(ϕp(uΔ∇))∇+a(t)f(t,u(t))=0,t∈[0,T]T,βu(0)−γuΔ(0)=0,u(T)=∑i=1m−2aiu(ξi),ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), whereϕp(s)isp-Laplacian operator, that is,ϕp(s)=|s|p−2s,p>1, ϕp−1=ϕq,1/p+1/q=1, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.
2003 ◽
Vol 46
(2)
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pp. 279-292
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2014 ◽
Vol 711
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pp. 303-307
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2009 ◽
Vol 2009
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pp. 1-12
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