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带有不同Hardy项的椭圆方程组的Mountain-Pass解 被引量:1
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作者 康东升 高蒙 +1 位作者 刘晓楠 曹玉平 《中南民族大学学报(自然科学版)》 CAS 2019年第2期304-308,共5页
研究了一类带有不同Hardy项和线性扰动项的临界椭圆方程组,解决了由不同Hardy项带来的困难,分析了相关最佳Sobolev常数达到函数的渐近性质.首次利用变分方法成功地证明了这类奇异椭圆方程组Mountain-Pass解的存在性.
关键词 椭圆方程组 临界 Hardy项 山路解
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求Duffing方程周期解的Mountain Pass方法 被引量:6
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作者 刘淑媛 吕显瑞 齐毅 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2007年第4期519-523,共5页
研究一类超线性Duffing方程周期解的存在性及其数值求解方法.利用山路引理证明了超线性Duffing方程周期解的存在性,并给出一种求Duffing方程周期解的Mountain Pass算法及其具体算例.
关键词 山路引理 临界点 P.S.条件 mountain pass算法 超线性Dulling方程
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Analysis of Remote Sensing Images of Ground Ruptures Resulting from the Kunlun Mountain Pass Earthquake in 2001 被引量:3
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作者 SHANXinjian LIJianhua +1 位作者 MAChao LIUJiahang 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2005年第1期43-52,共10页
On November 14, 2001, an earthquake measuring a magnitude of 8.1 occurred to the west of the Kunlun Mountain Pass which is near the border between Xinjiang and Qinghai of China. Since its epicenter is located in an ar... On November 14, 2001, an earthquake measuring a magnitude of 8.1 occurred to the west of the Kunlun Mountain Pass which is near the border between Xinjiang and Qinghai of China. Since its epicenter is located in an area at an elevation of 4900 m where the environment is extremely adverse, field investigation to this event seems very difficult. We have performed interpretation and analysis of the satellite images of ETM, SPOT, Ikonos, and ERS-1/2SAR to reveal the spatial distribution and deformation features of surface ruptures caused by this large earthquake. Our results show that the rupture zone on the ground is 426 km long, and strikes N90-110°E with evident left-lateral thrusting. In spatial extension, it has two distinct sections. One extends from the Bukadaban peak to the Kunlun Mountain Pass, with a total length of 350 km, and trending N95-110°E. Its fracture plane is almost vertical, with clear linear rupture traces and a single structure, and the maximum left-lateral offset is 7.8 m. This section is the main rupture zone caused by the earthquake, which is a re-fracturing along an old fault. The other is the section from Kushuihuan to the Taiyang Lake. It is 26 km long, trending N90-105°E, with the maximum strike-slip displacement being 3 m, and is a newly-generated seismic rupture. In a 50 km-long section between the Taiyang Lake and the Bukadaban peak, no rupture is found on the ground. The eastern and western rupture zones may have resulted from two earthquakes. The macroscopic epicenter is situated at 65 km east of the Hoh Sai Lake. The largest coseismic horizontal offset in the macroscopic epicenter ranges from 7 m to 8 m. Based on the dislocation partition of the whole rupture zone, it is suggested that this rupture zone has experienced a process of many times of intensification and fluctuation, exhibiting a remarkable feature of segmentation. 展开更多
关键词 satellite remote sensing EARTHQUAKE Kunlun mountain pass ground rupture zone
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Estimation of the stress levels in the focal region before and after the 2001 M=8.1 Western Kunlun Mountain Pass earth-quake
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作者 陈学忠 《Acta Seismologica Sinica(English Edition)》 EI CSCD 2005年第6期651-655,共5页
A method estimating the stress level in the focal region of an earthquake is proposed here. Taking the 2001 M=8.1 Western Kunlun Mountain Pass earthquake as an example, we estimate its stress level in the focal region... A method estimating the stress level in the focal region of an earthquake is proposed here. Taking the 2001 M=8.1 Western Kunlun Mountain Pass earthquake as an example, we estimate its stress level in the focal region before and after it by this method. The results show that the stress level in the focal region just prior to the initiation of this event is approximately 6.3-8 MPa, and about 5-6.7 MPa remained in the focal region after its occurrence. The stress in the focal region decreased by roughly twenty percent after this event. 展开更多
关键词 Western Kunlun mountain pass earthquake focal region stress level
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A discussion on Corioli force effect and aftershock activity tendency of the M=8.1 Kunlun Mountain Pass earthquake on Nov. 14, 2001
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作者 吕坚 高建华 +2 位作者 刘吉夫 胡翠娥 黄双凤 《Acta Seismologica Sinica(English Edition)》 CSCD 2003年第4期459-467,共9页
Following the theory and definition of the Corioli force in physics, the Corioli force at the site of the M=8.1 Kunlun Mountain Pass earthquake on November 14, 2001, is examined in this paper on the basis of a statist... Following the theory and definition of the Corioli force in physics, the Corioli force at the site of the M=8.1 Kunlun Mountain Pass earthquake on November 14, 2001, is examined in this paper on the basis of a statistical research on relationship between the Corioli force effect and the maximum aftershock magnitude of 20 earthquakes with M7.5 in Chinese mainland, and then the variation tendency of aftershock activity of the M=8.1 earthquake is discussed. The result shows: a) Analyzing the Corioli force effect is an effective method to predict maximum aftershock magnitude of large earthquakes in Chinese mainland. For the sinistral slip fault and the reverse fault with its hanging wall moving toward the right side of the cross-focus meridian plane, their Corioli force pulls the two fault walls apart, decreasing frictional resistance on fault plane during the fault movement and releasing elastic energy of the mainshock fully, so the maximum magnitude of aftershocks would be low. For the dextral slip fault, its Corioli force presses the two walls against each other and increases the frictional resistance on fault plane, prohibiting energy release of the mainshock, so the maximum magnitude of aftershocks would be high. b) The fault of the M=8.1 Kunlun Mountain earthquake on Nov. 14, 2001 is essentially a sinistral strike-slip fault, and the Corioli force pulled the two fault walls apart. Magnitude of the induced stress is about 0.06 MPa. After a comparison analysis, we suggest that the aftershock activity level will not be high in the late period of this earthquake sequence, and the maximum magnitude of the whole aftershocks sequence is estimated to be about 6.0. 展开更多
关键词 Corioli force effect aftershock magnitude M=8.1 Kunlun mountain pass earthquake Chinese mainland
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On Theorem of the “Mountain Im passe”Type
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作者 张宪君 戚桂杰 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第1期107-110, ,共4页
In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ ∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed f... In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ ∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed from c(R)>c 0. 展开更多
关键词 mountain Impasse”型定理 紧矩阵空间 非空闭子集
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Characteristics of Far-field Precursory Anomalies Before the M_S8.1 Earthquake in the West of Kunlun Mountains Pass
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作者 Chen Yuhua Dong Zhiping +1 位作者 Wang Peiling Li Yongqiang 《Earthquake Research in China》 2009年第3期354-371,共18页
In this study, a number of typical precursory anomalies recorded by stations in Qinghai, Gansu, Sichuan, Xinjiang, Ningxia, Hebei and Shaanxi provinces and autonomous regions before the M_S8.1 earthquake in the west o... In this study, a number of typical precursory anomalies recorded by stations in Qinghai, Gansu, Sichuan, Xinjiang, Ningxia, Hebei and Shaanxi provinces and autonomous regions before the M_S8.1 earthquake in the west of Kunlun Mountains Pass are collected and checked. According to the standards of earthquake cases in China, the criteria of the precursory anomalies are determined, and 53 distinguished. The characteristics of these anomalies before the M_S8.1 earthquake are analyzed, with results showing a very large earthquake affected area. The precursory anomalies recorded by instruments were 2900 km away from the epicenter, and according to the study in this paper, reached 2100 km away. The results also show that the anomalies present characteristics of long duration, multi-measurement items and large-amplitude variation. The authors believe that in large earthquake monitoring, attention should be paid to the variation of data over a large area, ranging up to thousands kilometers, with much denser earthquake observation networks. 展开更多
关键词 昆仑山口西8.1级地震 地震前兆异常 远场 特性 异常持续时间 昆仑山垭口 异常特征 地震影响
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Characteristics of Collapses Caused by the M8.1 Earthquake West of the Kunlun Mountains Pass
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作者 WangZanjun DangGuangming TianQinjian 《Earthquake Research in China》 2003年第4期352-363,共12页
An M 8.1 earthquake that occurred west of the Kunlun Mountains Pass has caused more than 20 collapse bodies or zones, which are mainly distributed near the surface seismic rupture zone, west of Hoh Sai Lake. The colla... An M 8.1 earthquake that occurred west of the Kunlun Mountains Pass has caused more than 20 collapse bodies or zones, which are mainly distributed near the surface seismic rupture zone, west of Hoh Sai Lake. The collapses are of four types, bedrock, soil mass and ice mass collapses and avalanches. The spatial distribution and the characteristics of development of the collapses are analyzed in the paper. Comparised with those caused by other earthquakes, the collapses are smaller in scale. In addition to the lithological characteristics of the crustal media, topographic, geomorphic and climatic factors, weaker seismic ground motion is an important cause for formation of the smaller-scale collapses. The long surface rupture zone and weaker ground motion are important features of the seismic rupture, which may be related to the structure of the preexisting fault. 展开更多
关键词 地震学 地震灾害 地震损失 昆仑山 地震断裂带
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The Frozen Soils and Devastating Characteristics of West Kunlun Mountains Pass M_S 8.1 Earthquake Area in 2001
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作者 ChenYongming WangLanmin +2 位作者 DaiWei WangWeifeng DaiHuaguang 《Earthquake Research in China》 2004年第4期337-347,共11页
The investigation on damages to frozen soil sites during the West Kunlun Mountains Pass earthquake with M S 8.1 in 2001 shows that the frozen soil in the seismic area is composed mainly of moraine, alluvial deposit, d... The investigation on damages to frozen soil sites during the West Kunlun Mountains Pass earthquake with M S 8.1 in 2001 shows that the frozen soil in the seismic area is composed mainly of moraine, alluvial deposit, diluvial deposit and lacustrine deposit with the depth varying greatly along the earthquake rupture zone. The deformation and rupture of frozen soil sites are mainly in the form of coseismic fracture zones caused by tectonic motion and fissures, liquefaction, seismic subsidence and collapse resulting from ground motion. The earthquake fracture zones on the surface are main brittle deformations, which, under the effect of sinistral strike-slip movement, are represented by shear fissures, tensional cracks and compressive bulges. The distribution and configuration patterns of deformation and rupture such as fissures, liquefaction, seismic subsidence and landslides are all related to the ambient rock and soil conditions of the earthquake area. The distribution of earthquake damage is characterized by large-scale rupture zones, rapid intensity attenuation along the Qinghai-Xizang (Tibet) Highway, where buildings distribute and predominant effect of rock and soil conditions. 展开更多
关键词 昆仑山垭口 地震 冻土 破坏特震 地表运动
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New Insight into the Surface Rupture Parameters of the Kunlun Mountains Pass M_S8.1 Earthquake
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作者 Tian Qinjian Zhang Liren +2 位作者 Hao Ping Wang Zanjun Wang Zhicai 《Earthquake Research in China》 2005年第3期282-291,共10页
Field observation shows that the surface rupture of the Kunlun Mountains Pass M_S 8.1 earthquake is about 426km long, and the maximum sinistral displacement is about 6m. Distribution of horizontal displacement along t... Field observation shows that the surface rupture of the Kunlun Mountains Pass M_S 8.1 earthquake is about 426km long, and the maximum sinistral displacement is about 6m. Distribution of horizontal displacement along the surface ruptures is markedly controlled by fault structure. The rupture length of this earthquake is significantly longer than statistic value. In this paper, using the method of “ultimate linear strain", we discussed the independency and integrality of the whole rupture zone and rupture segments of the Kunlun Mountains Pass earthquake by comparing with some large earthquakes on strike-slip faults on the Chinese continent. The conclusion is that the Kunlun Mountains Pass earthquake consists of successively triggered multiple earthquake events, other than a single earthquake event. 展开更多
关键词 昆仑山 地震 表面裂缝 震级
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R^(3)上具有一般凹凸非线性项的Klein-Gordon-Born-Infeld方程无穷多解的存在性
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作者 陈尚杰 《数学物理学报(A辑)》 CSCD 北大核心 2024年第3期637-649,共13页
该文运用临界点理论中的Z_(2)-山路定理得到了R^(3)上具有凹凸非线性项的Klein-Gordon方程和Born-Infeld理论耦合系统无穷多解的存在性.
关键词 KLEIN-GORDON方程 Born-Infeld理论 变分方法 Z_(2)-山路定理
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Effect of phase transition during roasting of Mountain Pass rare earth concentrate on leaching efficiency of rare earths
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作者 Yanyan Zhao Xu Sun +3 位作者 Deliang Meng Xiangsheng Liu Qiang Zhong Zongyu Feng 《Journal of Rare Earths》 SCIE EI CAS CSCD 2024年第2期409-414,I0006,共7页
To find a greener and more economical approach for treating the Mountain Pass rare earth concentrate(MPREC),a novel "Combination Method",including the processes of oxidizing roasting,HCI leaching and sulfuri... To find a greener and more economical approach for treating the Mountain Pass rare earth concentrate(MPREC),a novel "Combination Method",including the processes of oxidizing roasting,HCI leaching and sulfuric acid roasting,is proposed in this research.In this paper,the effect of phase transition behavior in hydrochloric acid leaching during oxidative roasting at 450-600℃ was studied.During roasting,the bastnasite in MPREC is decomposed into CeLa_(2)O_(3)F_(3) and(Ce_(0.33),La_(0.33),Ca_(0.33))O_(1.5).As the CeLa_(2)O_(3)F_(3) phase has the fluorine-fixation effect,the generated CeLa_(2)O_(3)F_(3) phase can not be dissolved by HCI after roasting at 500 and 550℃,but it can be decomposed by HCI after roasting at over 600℃,resulting in the improvement of the leaching rate of total F element.The maximum leaching efficiency of rare earth elements(REEs) can reach 70.32 wt% at the roasting temperature of 550℃.After roasting at over 600℃,some F^-ions in the solution combined with RE^(3+) to form REF_(3) precipitate and enter the leaching residue,and the others are in the form of [CeF_(3)]^+ in the leaching solution during leaching,therefore,the leaching efficiency of non-ce rium REEs decreases while that of cerium element increases.This work provides basic research for optimizing the actual production process of MPREC. 展开更多
关键词 mountain pass rare earth mine ROASTING Phase change Rare earths
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带有对数非线性项的双相问题非平凡解的存在性
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作者 熊明燕 储昌木 《贵州科学》 2024年第3期62-67,共6页
研究了一类带有对数非线性项的双相问题的非平凡解。通常的双相问题的非线性项是多项式形式,但是本文所处理的非线性项是对数非线性项。通过计算可知此类带有对数非线性项双相问题的能量泛函满足山路型结构,再利用序列的有界性得到了Pal... 研究了一类带有对数非线性项的双相问题的非平凡解。通常的双相问题的非线性项是多项式形式,但是本文所处理的非线性项是对数非线性项。通过计算可知此类带有对数非线性项双相问题的能量泛函满足山路型结构,再利用序列的有界性得到了Palais-Smale条件,最后结合山路引理,获得了该问题非平凡解的存在性结论。 展开更多
关键词 双相问题 对数非线性项 山路引理 非平凡解
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一类带扰动项的拟线性薛定谔方程的多解性
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作者 陈铭超 薛艳昉 《数学物理学报(A辑)》 CSCD 北大核心 2024年第2期417-428,共12页
该文研究了强制位势下非齐次拟线性薛定谔方程的多解性问题.通过山路定理和Ekeland变分原理,得到了该方程两个不同的解.所得结论是对此类拟线性方程已有结果的补充和推广.
关键词 拟线性薛定谔方程 非齐次 山路定理 EKELAND变分原理
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Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function
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作者 Jingxing Huang Junhui Xie 《Journal of Applied Mathematics and Physics》 2024年第7期2665-2681,共17页
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u,  x∈ℝN.(1)We first prove that the correspon... This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u,  x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1). 展开更多
关键词 Logarithmic Schrödinger Equations Weight Function Constrained Minimization Method Symmetric mountain pass Theorem
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一类具梯度项的分数阶椭圆方程解的存在性
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作者 潘柔 陈林 《长春师范大学学报》 2024年第2期7-12,共6页
运用山路定理与迭代的技巧证明下面分数阶椭圆方程:{(-Δ)_(p)^(s)u+V(x)u^(p-2)u=f(u,|▽u|^(p-2)▽u),u∈X^(s)(R^(N)),u(x)>0,x∈R^(N).正解的存在性,其中1<p<N,N≥2,0<s<1,(-Δ)_(p)^(s)是分数阶p-拉普拉斯算子,非... 运用山路定理与迭代的技巧证明下面分数阶椭圆方程:{(-Δ)_(p)^(s)u+V(x)u^(p-2)u=f(u,|▽u|^(p-2)▽u),u∈X^(s)(R^(N)),u(x)>0,x∈R^(N).正解的存在性,其中1<p<N,N≥2,0<s<1,(-Δ)_(p)^(s)是分数阶p-拉普拉斯算子,非线性项f:R×R^(N)→R是依赖于解的梯度项的连续函数,V(x)是正的连续函数. 展开更多
关键词 分数阶椭圆方程 山路定理 迭代法
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一类p-Laplacian的非齐次Kirchhoff-Schrödinger-Poisson系统的多重解研究
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作者 王梅 索洪敏 +1 位作者 张学梅 王臣熙 《数学理论与应用》 2024年第2期20-35,共16页
本文考虑如下p-Laplacian的非齐次拟线性Kirchhoff-Schr?dinger-Poisson系统解的存在性:{-(a-b∫_(R^(3))|■u|^(p)dx)△_(p)u+|u|^(p-2)u+λφ_(u)u=|u|^(q-2)u+h(x),x∈R^(3),-△_(φ)=u^(2),其中a,b>0,4/3<p<12/5,p<q<... 本文考虑如下p-Laplacian的非齐次拟线性Kirchhoff-Schr?dinger-Poisson系统解的存在性:{-(a-b∫_(R^(3))|■u|^(p)dx)△_(p)u+|u|^(p-2)u+λφ_(u)u=|u|^(q-2)u+h(x),x∈R^(3),-△_(φ)=u^(2),其中a,b>0,4/3<p<12/5,p<q<p^(*)=3p/3-p,λ>0.当h(x)满足适当的条件时,运用Ekeland变分原理和山路定理给出系统多重解的存在性. 展开更多
关键词 Kirchhoff-Schrödinger-Poisson系统 P-LAPLACIAN EKELAND变分原理 山路定理
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一类分数阶p-拉普拉斯方程组解的存在性
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作者 潘柔 陈林 《伊犁师范大学学报(自然科学版)》 2024年第1期27-34,61,共9页
主要研究一类分数阶p-拉普拉斯方程组边值问题,运用山路定理与埃克兰变分原理,证明了该方程组至少存在两个非平凡的弱解.
关键词 p-拉普拉斯方程组 山路定理 埃克兰变分原理
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一类变号位势的Klein-Gordon-Maxwell系统解的存在性和多重性
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作者 孙歆 《贵州工程应用技术学院学报》 2024年第3期1-8,共8页
研究一类含有参数的Klein-Gordon-Maxwell系统解的存在性和多重性。当非线性项满足一般超线性条件且位势是允许变号时,利用变分法和分析技巧获得了系统解的存在性和多重性结果,完善了此系统解的存在性的已有结果。
关键词 Klein-Gordon-Maxwell系统 变分法 山路定理
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一类带有临界指数的分数阶Schrodinger-Poisson系统正解的存在性
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作者 廖家锋 蒋维 《西华师范大学学报(自然科学版)》 2024年第1期31-38,共8页
分数阶Schrodinger-Poisson系统是由分数阶Schrodinger方程和分数阶Poisson方程耦合而成。本文考虑了含有临界指数的分数阶Schrodinger-Poisson系统,由于非局部项中含有临界指数,这使得对(PS)c条件的成立和山路水平值的估计有一定的困... 分数阶Schrodinger-Poisson系统是由分数阶Schrodinger方程和分数阶Poisson方程耦合而成。本文考虑了含有临界指数的分数阶Schrodinger-Poisson系统,由于非局部项中含有临界指数,这使得对(PS)c条件的成立和山路水平值的估计有一定的困难。通过山路定理和变分方法,得到了该系统正解的存在性。补充并推广了以往分数阶Schrodinger-Poisson系统的相关结论。 展开更多
关键词 正解 临界指数 分数阶Schrodinger-Poisson系统 山路定理
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