Name
Title | ||
|---|---|---|
Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives. |
Abstract | ||
|---|---|---|
In this work, we establish the existence of multiple positive solutions for a general higher order fractional differential equation with derivatives and a sign-changing Carathèodory perturbed term-Dαx(t)=p(t)ft,x(t),Dμ1x(t),Dμ2x(t),…,Dμn-1x(t)-gt,x(t),Dμ1x(t),Dμ2x(t),…,Dμn-1x(t),Dμix(0)=0,1⩽i⩽n-1,Dμn-1+1x(0)=0,Dμn-1x(1)=∑j=1m-2ajDμn-1x(ξj),where n-1<α⩽n,n∈N and n⩾3 with 0<μ1<μ2<⋯<μn-2<μn-1 and n-3<μn-1<α-2,aj∈R,0<ξ1<ξ2<…<ξm-2<1 satisfying 0<∑j=1m-2ajξjα-μn-1-1<1, Dα is the standard Riemann–Liouville derivative, f∈C([0,1]×Rn,[0,+∞)). This equation is viewed as a perturbation of a general higher order fractional differential equation, where the perturbed term g:[0,1]×Rn→(-∞,+∞) only satisfies the global Carathéodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.amc.2012.07.046 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Fractional differential equation,Singularly perturbed problems,Positive solutions,Fixed point theory,Carathéodory’s conditions | Extended real number line,Differential equation,Mathematical optimization,Nonlinear system,Mathematical analysis,Mathematics,Fixed-point theorem | Journal |
Volume | Issue | ISSN |
219 | 4 | 0096-3003 |
Citations | PageRank | References |
10 | 0.65 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xinguang Zhang | 1 | 163 | 23.65 |
| Lishan Liu | 2 | 188 | 35.41 |
| Yonghong Wu | 3 | 212 | 34.70 |