研究一类非线性分数阶微分方程m点边值问题:D_(0+)~αu(t)+h(t)f(t,u(t),D_(0+)~βu(t))=0,0<t<1,其中,u(0)=u'(0)=…=u^(n-2)(0)=0,D_(0+)~βu(1)=sum from j=1 to m-2 (η_jD_(0+)~βu(ζ_j)).D_(0+)~αu(t)和D_(0+)~βu(t...研究一类非线性分数阶微分方程m点边值问题:D_(0+)~αu(t)+h(t)f(t,u(t),D_(0+)~βu(t))=0,0<t<1,其中,u(0)=u'(0)=…=u^(n-2)(0)=0,D_(0+)~βu(1)=sum from j=1 to m-2 (η_jD_(0+)~βu(ζ_j)).D_(0+)~αu(t)和D_(0+)~βu(t)是标准Riemann-Liouville分数阶导数,α≥2,n-1<α≤n,β≥1,α-β≥1,0≤η_j(j=1,2,…,m-2),0<ζ_1<ζ_2<…<ζ_(m-2)<1,1-sum from j=1 to m-2 (η_jζ_j^(α-β-1)>0).利用不动点理论,得到正解的存在性、唯一性和多解性的一些充分条件,最后,通过一些具体的数字例验证了结果.展开更多
文摘研究一类非线性分数阶微分方程m点边值问题:D_(0+)~αu(t)+h(t)f(t,u(t),D_(0+)~βu(t))=0,0<t<1,其中,u(0)=u'(0)=…=u^(n-2)(0)=0,D_(0+)~βu(1)=sum from j=1 to m-2 (η_jD_(0+)~βu(ζ_j)).D_(0+)~αu(t)和D_(0+)~βu(t)是标准Riemann-Liouville分数阶导数,α≥2,n-1<α≤n,β≥1,α-β≥1,0≤η_j(j=1,2,…,m-2),0<ζ_1<ζ_2<…<ζ_(m-2)<1,1-sum from j=1 to m-2 (η_jζ_j^(α-β-1)>0).利用不动点理论,得到正解的存在性、唯一性和多解性的一些充分条件,最后,通过一些具体的数字例验证了结果.
