一类半正非线性弹性梁方程边值问题正解的存在性

Existence of positive solutions for a class of semi-positive nonlinear elastic beam equation boundary value problems

运用锥上的不动点定理获得了带Neumann边界条件的半正非线性弹性梁方程边值问题{y^(4)(x)+(k1+k2)y″(x)+k1 k2 y(x)=λf(x,y(x)),x∈[0,1],y′(0)=y′(1)=y^■(0)=y^■(1)=0{在条件0<k1<k2≤π24下正解的存在性和多解性,其中λ>0,f∈C([0,1]×[0,∞),(-∞∞))存在正常数X使得f(x,y)≥-X成立。

By using the fixed point theorem of cone mapping,it obtains the existence and multiplicity of positive solutions for the semipositive nonlinear elastic beam equation boundary value problems {y^(4)(x)+(k1+k2)y″(x)+k1 k2 y(x)=λf(x,y(x)),x∈[0,1],y′(0)=y′(1)=y^■(0)=y^■(1)=0{with Neumann boundary conditions,where 0<k1<k2≤π^2/4,λ>0 is a parameter and f∈C([0,1]×[0,∞),(-∞,∞)),with f(x,y)≥-X for some positive constant X.