【摘要】 本文考虑了四阶非线性特征值问题 d4u/dt4=λg(t)f(u,u"),0<t<1, u(0)=u(1)=0, au"(0)-bu""(0)=0,cu"(1)+du"’(1)=0.其中g(t)∈C((0,1),[0,∞)),f(u,v)∈C([0,∞)×(-∞,0],[0,∞)),a ≥ 0,b≥0,c≥0,d ≥ 0,且△=ac+ad+bc>0.利用锥压缩与拉伸不动点定理,获得了上述问题正解的存在性结果.更多还原

【Abstract】 The paper investigates the fourth-order nonlinear eigenvalue problemd4u/dt4 = λg(t)f(u,u"), 0<t<l,u(0) = u(1) = 0,au"(0) - bu’"(0) = 0, cu"(1) + du’"(1) = 0.Existence of the positive solution for the problem by employing the fixed-point theorem of cone expansion and compression type is obtained.更多还原