关键词: 单侧全局区间分歧, 半线性问题, 定号解, 周期问题

Abstract: 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=???20170511-1???f(s)/s,f_∞=???20170511-2???f(s)/s.

Key words: Unilateral interval bifurcation, Half-linear problems, One-sign solutions, Periodic problems