In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an exam...In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an example, a three pointboundary value problem of second order differential equations is considered inthis paper and all of the results obtained by the Wirtinger type inequalities anddifferential inclusions in Gupta [5] and Marano [11] will be improved.展开更多
A new simplicial homtopy algorithm is presented for computing the Leray-Schauder fixed points as well as Merrill fixed points and Eaves fixed points. Moreover, a coercivity condition to guarantee the computation proce...A new simplicial homtopy algorithm is presented for computing the Leray-Schauder fixed points as well as Merrill fixed points and Eaves fixed points. Moreover, a coercivity condition to guarantee the computation proceeding in a bounded region is given.展开更多
运用Leray-Schauder度理论和不动点定理获得了两端固定支撑边界条件下四阶变系数常微分系统固结梁边值问题{ u(4)(x)+a(x)u(x)=f1(x,v(x)), x∈(0,1),v(4)(x)+b(x)v(x)=f2(x,u(x)), x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,v(0)=v(1)=v′(0...运用Leray-Schauder度理论和不动点定理获得了两端固定支撑边界条件下四阶变系数常微分系统固结梁边值问题{ u(4)(x)+a(x)u(x)=f1(x,v(x)), x∈(0,1),v(4)(x)+b(x)v(x)=f2(x,u(x)), x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,v(0)=v(1)=v′(0)=v′(1)=0正解的存在性和唯一性,其中a,b:[ 0,1 ]→[ 0,+∞ )连续,非线性项fi:[ 0,1 ]×R→R为连续函数且fi(x,0)≥0 (i=1,2)。The existence and uniqueness of positive solution for the boundary value problem of fourth order variable coefficients ordinary differential system{ u(4)(x)+a(x)u(x)=f1(x,v(x)), x∈(0,1),v(4)(x)+b(x)v(x)=f2(x,u(x)), x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,v(0)=v(1)=v′(0)=v′(1)=0with clamped beam conditions were obtained using Leray-Schauder degree theory and fixed point theorem, where a,b:[ 0,1 ]→[ 0,+∞ )are continuous, nonlinear term fi:[ 0,1 ]×R→Rare continuous and fi(x,0)≥0 (i=1,2).展开更多
文摘In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an example, a three pointboundary value problem of second order differential equations is considered inthis paper and all of the results obtained by the Wirtinger type inequalities anddifferential inclusions in Gupta [5] and Marano [11] will be improved.
文摘A new simplicial homtopy algorithm is presented for computing the Leray-Schauder fixed points as well as Merrill fixed points and Eaves fixed points. Moreover, a coercivity condition to guarantee the computation proceeding in a bounded region is given.
文摘运用Leray-Schauder度理论和不动点定理获得了两端固定支撑边界条件下四阶变系数常微分系统固结梁边值问题{ u(4)(x)+a(x)u(x)=f1(x,v(x)), x∈(0,1),v(4)(x)+b(x)v(x)=f2(x,u(x)), x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,v(0)=v(1)=v′(0)=v′(1)=0正解的存在性和唯一性,其中a,b:[ 0,1 ]→[ 0,+∞ )连续,非线性项fi:[ 0,1 ]×R→R为连续函数且fi(x,0)≥0 (i=1,2)。The existence and uniqueness of positive solution for the boundary value problem of fourth order variable coefficients ordinary differential system{ u(4)(x)+a(x)u(x)=f1(x,v(x)), x∈(0,1),v(4)(x)+b(x)v(x)=f2(x,u(x)), x∈(0,1),u(0)=u(1)=u′(0)=u′(1)=0,v(0)=v(1)=v′(0)=v′(1)=0with clamped beam conditions were obtained using Leray-Schauder degree theory and fixed point theorem, where a,b:[ 0,1 ]→[ 0,+∞ )are continuous, nonlinear term fi:[ 0,1 ]×R→Rare continuous and fi(x,0)≥0 (i=1,2).
