JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Periodic solutions for a class of Kirchhoff-type differential systems

ZHANG Shen-gui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 1-6. doi:10.6040/j.issn.1671-9352.0.2018.131

Abstract ( 1200 )

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By using variational principle, the author studied periodic solutions for a class of superlinear Kirchhoff-type p(t)-Laplacian systems. Under the condition of no Ambrosetti-Rabinowitz-type growth, some results for the existence of periodic solutions are obtained by means of a variant mountain pass type theorem.

Existence of positive solutions to a semipositone second-order boundary value problem

WEI Jin-ying, WANG Su-yun, LI Yong-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 7-12. doi:10.6040/j.issn.1671-9352.0.2018.263

Abstract ( 1026 )

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We consider the existence of positive solutions to the boundary value problemu″(t)+c(t)u+λf(t,u)=0, 0<t<1, u(0)=u(1)=0,where λ>0, c(·)∈C［0,1］ satisfies -∞<c(t)<π² for t∈［0,1］, f:［0,1］×R⁺→R is continuous function and satisfies f≥-L, L>0 is a constant. By investigating the sign property of the Green function of the associated linear boundary value problem, we show the existence of positive solutions of semipositone problems. The proof of the main result is based on Krasnoselskii fixed point theorems in cone.

Existence of mild solutions for a class of fractional stochastic evolution equations with nonlocal initial conditions

CHEN Peng-yu, MA Wei-feng, Ahmed Abdelmonem

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 13-23. doi:10.6040/j.issn.1671-9352.0.2019.140

Abstract ( 1026 )

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This paper obtains the existence results of mild solutions to a class of fractional stochastic evolution equations with nonlocal conditions by applying stochastic analysis theory, Schauder fixed point theorem and approximation method assumes that the nonlinear term is Carethéodory continuous and satisfies some weak growth condition, the nonlocal term depends on all the value of independent variable on the whole interval and satisfies some weak growth condition. This work may be viewed as an attempt to develop a general existence theory for fractional stochastic evolution equations with general nonlocal conditions. Finally, as a sample of application, the results are applied to a fractional stochastic partial differential equation with nonlocal integral condition.

Existence of solutions for non-coercivity quasilinear elliptic equations with Hardy potential

XIAWU Ji-mao, HUANG Shui-bo, DENG De-jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 24-32. doi:10.6040/j.issn.1671-9352.0.2018.671

Abstract ( 1025 )

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This paper studies the existence and regularity of solutions to non-coercivity quasilinear elliptic problems with lower order terms and the Hardy potential, and focuses on the regularizing effect of lower order terms and the influence of the Hardy potential.

Existence of positive solutions for boundary value problems of third-order delay differential equations

LUO Qiang, HAN Xiao-ling, YANG Zhong-gui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 33-39. doi:10.6040/j.issn.1671-9352.0.2019.031

Abstract ( 1081 )

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By applying the fixed point theorem on the cone, this paper studies the existence of positive solutions for boundary value problems of third-order delay differential equation{u(t)+λa(t)f(t,u(t-τ))=0, t∈(0,1),τ>0,u(t)=0,-τ≤t≤0,u(0)=u″(0)=0,u(1)=αu(η)where λ is parameter, and 0<η<1, 0<α<1/η, f:［0,1］×［0,∞］→［0,∞) is continuous.

Existence of positive solution for a class of N-Kirchhoff type equation

CHEN Lin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 40-48. doi:10.6040/j.issn.1671-9352.0.2019.157

Abstract ( 808 )

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This paper studies the existence of positive solution for a class of N-Kirchhoff type problem whose nonlinearity depends on the gradient of the solution. Applying a variational method and an iterative technique, the analysis proves that the problem has at least one positive week solution.

Eigenvalues asymptotic formula and trace formula for a class of impulsive Sturm-Liouville operators

JI Jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 49-56. doi:10.6040/j.issn.1671-9352.0.2018.760

Abstract ( 1204 )

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A class of impulsive Strum-Liouville boundary value problems on a finite interval are discussed, there are discontinuities inside the interval and the discontinuity coefficient on the right side of the equation. The asymptotic formula of the eigenvalues and the trace formula are obtained by using the residue theorem.

Existence of positive solutions for fractional nonhomogeneous boundary value problem with p-Laplacian

SONG Jun-qiu, JIA Mei, LIU Xi-ping, LI Lin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 57-66. doi:10.6040/j.issn.1671-9352.0.2018.302

Abstract ( 1182 )

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We study the existence of positive solutions for integral boundary value problem of fractional p-Laplacian equation with disturbance parameters. According to the properties of integral kernel and using the cone expansion and cone compression fixed point theorem and the super-linear and sub-linear conditions, the sufficient conditions of existence and nonexistence of positive solutions for the boundary value problem are obtained. The conclusions show the impact of parameters on the existence of positive solutions. Finally, we give some examples to illustrate our main results.

Study on nonlinear HIV/AIDS model with two infection stages treatment and incidence rate

WANG Fei, YANG Ya-li, JIN Ying-ji, CAO Shu-miao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 67-73. doi:10.6040/j.issn.1671-9352.1.2019.037

Abstract ( 1115 )

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Based on the actual transmission and treatment, a mathematical model of HIV/AIDS with two infection stages, treatment and non-linear incidence is established in this paper.Then the range of the feasible region of the system is discussed by using the limit theory.Secondly, the basic regeneration number is obtained by constructing regeneration matrix, and the range of the basic regeneration number is discussed. The existence and number of equilibrium points are obtained.Finally, the local and global properties of equilibrium point are proved by constructing Lyapunov function, using Lasalle invariant set, Boosenberg theorem and Van den Lacy principle.

Existence of nontrival solutions for a class of Schrödinger-Poisson systems

CHEN Li-zhen, FENG Xiao-jing, LI Gang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 74-78. doi:10.6040/j.issn.1671-9352.0.2018.638

Abstract ( 1256 )

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We investigate a class of Schrödinger-Poisson systems, by means of variational method and critical point theory. Here, the Poisson term is a more general form. By adding quasi-critical growth and AR conditions to the nonlinear term, we prove the existence of nontrival solution of the system. The result supplement and promote the previous resluts on the Schrödinger-Poisson systems.

Higher ξ-Lie derivable maps on triangular algebras at reciprocal elements

ZHANG Xia, ZHANG Jian-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 79-84. doi:10.6040/j.issn.1671-9352.0.2019.192

Abstract ( 1086 )

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Let U=Tri(A,M,B )be a triangular algebra with identity 1, 1_A,1_B be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k1,k2 respectively, making k₁1_A-A, k₂1_B-B invertible in triangular algebras. {φ_n}_n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φ_n}_n∈N satisfies φ_n(［U,V］_ξ)=∑_i+j=nφ_i(U)φ_j(V)-ξφ_i(V)φ_j(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then {φ_n}_n∈N is a higher derivation, where φ0=id0 is the identity map, ［U,V］_ξ=UV-ξVU.

Additivity of biderivable maps on generalized matrix algebras

FEI Xiu-hai, DAI Lei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 85-90. doi:10.6040/j.issn.1671-9352.0.2018.635

Abstract ( 1028 )

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Let G be a generalized matrix algebra, φ:G ×G →G be a mapping of G(without assumption of additivity on each argument). if φ satisfies φ(XY,Z)=φ(X,Z)Y+Xφ(Y,Z)and φ(X,YZ)=φ(X,Y)Z+Yφ(X,Z)for all X,Y,Z∈G, then φ is a biderivation.

Local existence and uniqueness of positive solutions for a Sturm-Liouville boundary value problem of second order differential equations

ZHU Xiao-lin, ZHAI Cheng-bo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 91-96. doi:10.6040/j.issn.1671-9352.0.2018.561

Abstract ( 1655 )

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The positive solution of a class of second-order nonlinear differential equation with Sturm-Liouville boundary value conditions is studied. By using fixed point theorems in ordered Banach spaces, the local existence and uniqueness of positive solutions is given. Finally, two applied examples are given.

Almost automorphic solutions for shunting inhibitory cellular neural networks with leakage delays on time scales

DAI Li-hua, HUI Yuan-xian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 97-108. doi:10.6040/j.issn.1671-9352.0.2018.600

Abstract ( 1078 )

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Shunting inhibitory cellular neural networks(SICNNs)with time-varying delays in the leakage term and continuously distributed delays on time scale T is proposed. Based on the exponential dichotomy of linear dynamic equation on time scales, fixed point theorems on time scales, we obtain some new sufficient conditions for the existence a global exponential stability of almost automorphic solution for the class of neural networks. Moreover, we give convictive numerical examples to show the feasibility of our results. This paper contains the several classes of functional differential equations, including the existence of solutions and the stability of this solution on time scales. Also, some new results are obtained.

Coleman automorphisms of extensions of the finite groups by some groups

ZHAO Le-le, HAI Jin-ke

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 109-112. doi:10.6040/j.issn.1671-9352.0.2018.673

Abstract ( 1153 )

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Let G be an extension of a finite characteristically simple group by a finite abelian group or a finite non-abelian simple group. It is shown that under some conditions all Coleman automorphism of G is an inner automorphism.

Rules acquisition of decision formal contexts based on attribute granular

QIAN Ting, ZHAO Si-yu, HE Xiao-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 113-120. doi:10.6040/j.issn.1671-9352.1.2019.011

Abstract ( 1082 )

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As a hot research topic, granular computing makes the multi-level research questions possible. If granular computing is introduced to decision formal context, there are more accurate decision rules. In this paper, we define the multiple granularity decision formal context from the perspective of granularity of a g-tree, then the consistent properties between before and after granulation are studied. The relationship between rules of before and after granulation are given.

Quantum steering of mutually unbiased measurements

ZHANG Qiang-qiang, CHEN Zheng-li, YUAN Feng-ru

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10): 121-126. doi:10.6040/j.issn.1671-9352.0.2018.503

Abstract ( 1176 )

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Based on the study of some properties of the quantum steering and the mutually unbiased measurements, we have given the quantum steering of separable states, pure entangled states and Bell-diagonal states under mutually unbiased measurements.

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