徐佳宁;何延生;

• 1:延边大学理学院

摘要(Abstract)：

研究一类非线性高阶q-对称差分方程解的存在性,通过计算得出解的表达形式,利用Banach空间完全连续算子的不动点定理得出解的存在唯一性结果,应用Schaefer's不动点定理得出解的存在性。

关键词(KeyWords)：q-对称差分方程;解的唯一性;不动点定理;解的存在性

Abstract:

Keywords:

基金项目(Foundation):国家自然科学基金项目(11161049)

作者(Author):徐佳宁;何延生;

Email:

参考文献(References)：

• [1]Page D N.Information in black hole radiation[J].Physical Review letters,1993,71(23):3743-3746.

• [2]Donam Y.q-deformed conformal quantum mechanics[J].Physical Review D,2000,62(9):276-284.

• [3]Jordan C.Calculus of finite differences[M].New York:Chelsea Publishing Company,1950:141-145.

• [4]Ernst T.The different tongues of q-calculus[J].Proceedings of Estonian Academy of Sciences,2008,57(2):81-99.

• [5]Koekoek R,Lesky P A.Hypergeometric orthogonal polynomials and their q-Analogues[M].Springer Berlin Heidelberg:American Mathematical Society,2010:413-552.

• [6]Jackon F H.q-difference equations[J].American Journal of Mathematics,1910,32(4):305-314.

• [7]Lavagno A,Gervino G.Quantum mechanics in q-deformed calculus[J].Journal of Physics Conference Series,2009,174(1):223-239.

• [8]Jackson G H.On a q-definite integrals[J].The Quarterly Journal of Pure and Applied Mathematics,1910(41):193-203.

• [9]Brito D C A M C,Martins N.The q-symmetric variational calculus[J].Computers and Mathematics with Applications,2012,64(7):2241-2250.

• [10]徐佳宁,侯成敏.一类二阶q-对称差分方程两点边值问题解的存在性[J].延边大学学报:自然科学版,2015,41(3):189-195.Xu Jianing,Hou Chengmin.Existence of solutions for a class of q-symmetric difference equation two points boundary value problem[J].Journal of Yanbian University:Natural Science,2015,41(3):189-195.

• [11]张瑜,侯成敏.带有p-Laplacian算子的分数阶多点边值问题单调正解的存在性[J].东北石油大学学报,2014,38(6):116-125.Zhang Yu,Hou Chengmin.Existence of monotone positive solution for fractional multipoint boundary value problem with p-Laplacian operator[J].Journal of Northeast Petroleum University,2014,38(6):116-125.

• [12]Gasper G,Rahman M.Basic hypergeometric series[M].Basic Hypergeometric Series:Cambrige University Press,1990:175-203.

• [13]Hahn W.Lineare Geometrische Differencezengleichungen[J].Ferschungszentrum Graz-Statistische Sektion,1981(66):48-56.

• [14]Zhang Xinguang,Liu Lishan,Benchawan W,et al.The eigenvalue for a class of singular P-Laplacian fractional differential equations involving the Riemnn-Stieltjes integral boundary condition[J].Applied Mathematics and Computation,2014,235(4):412-422.

• [15]Benchohra M,Hamani S,Ntouyas S K.Boundary value problems for differential equitions with fractional order and nonlocal conditions[J].Surveys in Mathematics and Its Applications,2008,71(7-8):2391-2396.