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§ 1. IntroductionThepurposeofthispaperistostudytheoscillatorybehaviorofsolutionsofcertainquasi linearellipticequationsdiv( |Du|m -2 A(x)Du) + p(x) |u|m -2 u=0 ,x∈Ω Rn,(E)whereΩisanexteriordomain ,m >1 ,andfunctionsA(x) ,p(x)aretobespecifiedinthefollowingtext.Recently ,USAMI [6]consideredEq .(E)whenA(x)≡I (identitymatrix) ,andob tainedoscillationcriteriaforEq .(E)with“infiniteintegral”coefficient [cf.[6],Theorem 4].However,asfarasthepresentreferencesisconcerned ,therearefewo… 相似文献
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By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order. 相似文献
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Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples. 相似文献
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考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E),其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则. 相似文献
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In this paper, we present some new asymptotic results for a second order elliptic differential equations by using integral averaging and completing square technique. 相似文献
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具有“弱积分小”系数的二阶椭圆型偏微分方程解的振动性质 总被引:7,自引:1,他引:6
本文考虑二阶非线性椭圆型偏微分方程解的振动性质,得到了在具有“弱积分小”系数条件下,所有解均振动的充分准则,这些结果在很大程度上改进和推广了具有“积分小”系数的二阶常微分方程的振动结果. 相似文献
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER NONLINEAR ELLIPTIC DIFFERENTIAL EQUATIONS 总被引:1,自引:0,他引:1
徐志庭 《数学物理学报(B辑英文版)》2001,21(1)
1 IntroductionTlle problem of obtaining sufficient conditions to ensure that al1 solutions of second orderordinary differential equations with an "integrally smal" coefficiellt are oscillatory'has beenstudied by many authors [cft1-4]] and other referellces cited therein. Recently, the paPers[cf[5],[6]] have discussed the asymptotiC properties of the solutions Of the follOwing equatious(a(f)W(x)X,), q(t)i(x) = c(t),(g(f, T)X,), q(t)f(x) = e(t),here q(f) is allowed to challge sign. In thi… 相似文献
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1 IntroductionRecently, the papers (cf [1], [2]) have established stabi1ity of p-NFDEsusing Liapunov-Razumikhin functionaJs. However, in order to study the limtset and the existence of periodic solutions of p-NFDEs, we need to know notonly the stability but ajso the boundedness of solutions. In this paper, weshal1 discuss the boundedness properties of P-NFDEs by Liapunov functionals,which improve some boundedness conditions for FDEs in the literature. Someexamples are also worked out t… 相似文献