Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator
2010 ◽
Vol 2010
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pp. 1-17
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Keyword(s):
We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0,0<t<1,u(0)=u′(1)=0,u′′(0)=0,D0+αu(t)|t=0=0, where0<γ<1,2<α<3,0<ρ⩽1,D0+αdenotes the Caputo derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous function,ϕp(s)=|s|p-2s,p>1, (ϕp)-1=ϕq, 1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.
2011 ◽
Vol 38
(1-2)
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pp. 225-241
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2010 ◽
Vol 18
(3)
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pp. 327-339
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2013 ◽
Vol 23
(1)
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pp. 43-56
Positive solutions to singular boundary value problem for nonlinear fractional differential equation
2010 ◽
Vol 59
(3)
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pp. 1300-1309
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