摘要:首先建立一类含不可微非线性项周期问题的单侧全局区间分歧定理.应用上述定理,可以证明一类半线性周期问题主半特征值的存在性.进而,可研究下列半线性周期问题定号解的存在性-x″+q(t)x=αx++βx-+ra(t)f(x),0<t<T,x(0)=x(T),x'(0)=x'(T),其中r≠0是一个参数,q,a∈C([0,T],(0,∞)),α,β∈C[0,T],x+=max{x,0},x-=-min{x,0};f∈C(R,R),当s≠0时,sf(s)>0成立,并且f0∈[0,∞)且f∞∈(0,∞)或f0∈[0,∞]且f∞=0,其中f0 =|lim|s|→0f(s)/s,f∞=lim|s|→+∞f(s)/s.%In this paper,we establish a unilateral global bifurcation result from interval for a class of periodic problems with nondifferentiable nonlinearity.By applying the above result,we shall prove the existence of the principal half-eigenvalues for a class of half-linear periodic boundary problems.Moreover,we also investigate the existence of one-sign solutions for the following half-linear periodic problems.-x″ + q(t)x =αx+ +βx-+ ra(t)f(x),0 < t < T,x(0) =x(T),x'(0) =x'(T),where r ≠ 0 is a parameter,q,a ∈ C([0,T],(0,∞)),α,β ∈ C[0,T],x+ =max{x,0},x-=-min{x,0};f ∈ C(R,R),sf(s) > 0 for s ≠ 0,and f0 ∈ [0,∞) and f∞ ∈ (0,∞) or f0 ∈ [0,∞]and f∞ =0,where f0 =lim |s|→0f(s)/s,f∞ =lim|s|→+∞ f(s)/s.