Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions

[摘要] We study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditionsu′′′′(t)=λf(t,u(t)),  t∈(0,1),u(0)=0,  u′(0)=μh(u(0)),  u′′(1)=0,  u′′′(1)=μg(u(1)), whereλ>0, μ≥0are parameters, andf:0, 1×0,+∞→0, +∞, h:0, +∞→0, +∞, andg:0, +∞→-∞,0are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution forλ,  μsufficiently small and has no positive solution forλlarge enough.

[学科分类] 应用数学