【摘要】：首先建立一類含不可微非線性項(xiàng)周期問題的單側(cè)全局區(qū)間分歧定理.應(yīng)用上述定理,可以證明一類半線性周期問題主半特征值的存在性.進(jìn)而,可研究下列半線性周期問題定號解的存在性-x″+q(t)x=αx~++βx~-+ra(t)f(x),0tT,x(0)=x(T),x'(0)=x'(T),其中r≠0是一個參數(shù),q,a∈C([0,T],(0,∞)),α,β∈C[0,T],x~+=max{x,0},x~-=-min{x,0};f∈C(R,R),當(dāng)s≠0時,sf(s)0成立,并且f0∈[0,∞)且f_∞∈(0,∞)或f_0∈[0,∞]且f_∞=0,其中f0=lim"#s"#→0f(s)/s,f_∞=lim"#s"#→+∞f(s)/s.
[Abstract]:Firstly, a class of unilateral global interval bifurcation theorem for periodic problems with nondifferentiable nonlinear terms is established. By using the above theorem, the existence of principal semi-eigenvalues for a class of semilinear periodic problems can be proved. Furthermore, we can study the existence of signed solutions for the following semilinear periodic problems-x "q (t) x = 偽 x 尾 x 鈮，

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