一类具非局部边界条件的四阶非线性微分方程的对称正解

本文考虑形如的非线性四阶微分方程非局部边值问题,这里a,b∈L~10,1],g:(0,1)→0,∞)在(0,1)上连续、对称,且可能在t=0和t=1处奇异．f:0,1]×0,∞)→0,∞)连续且对所有x∈0,∞],f(·,x)在0,1]上对称．在某些适当的增长性条件下,应用Krasnoselskii不动点定理证明了对称正解的存在性和多重性．

Symmetric Positive Solutions to a Fourth-Order Nonlinear Differential Equation with Nonlocal Boundary Conditions

We consider the nonlocal boundary value problem for a nonlinear fourth- order ordinary differential equation of the form where a,b E L~10,1],g:(0,1)→0,∞) is continuous,symmetric on (0,1) and maybe singular at t=0 and t=1.f:0,1]×0,∞)→0,∞) is continuous and f(·,x) is symmetric on 0,1] for all x E 0,∞).Under some suitable growth conditions,we show the existence and multiplicity of symmetric positive solutions of that above problem by applying Krasnoselskii's fixed point theorem in a cone.