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In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω. 相似文献
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利用锥上的不动点定理研究周期边值问题:Lu:u″+m2u=f(t,u(t),u′(t)),u(0)=u(2π),u′(0)=u′(2π),其中,m∈0,12的正解的存在性,并获得了一些新的结论. 相似文献
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研究了在(0,∞)×Rn上,变系数耗散波动方程的能量在外区域上的衰减估计,得到:若初值{u0,u1}属于能量空间且具有紧支集,则在Rn上存在一个外区域Xm,使得对任意t ≥ 0和m>0,有进一步,若u0+u1=0,还可以得到∫Xm|u|2dx ≤ C(1+t)-m,t ≥ 0. 相似文献
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