四阶差分方程周期边值问题的Green函数
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摘要
本文研究了四阶差分方程周期边值问题的Green函数.得到了一些新的结果,推广了A. Cabada和N. Dimitrov论文中一些结果.
In this paper, we study the Green's function of fourth-order difference equation with periodic boundary value problem. We obtain some new results and generalize some main results in A. CabadaandN. Dimitrov's paper.
In this paper, we study the Green's function of fourth-order difference equation with periodic boundary value problem. We obtain some new results and generalize some main results in A. CabadaandN. Dimitrov's paper.
引文
[1]Gupta, C P. Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems. Appl. Anal., 36:157-169(1990)
[2]Peletier, L A, Rodrígues, J A. Homoclinic orbits to a saddle-center in a fourth-order differential equation. J. Differential Equations, 203:185-215(2004)
[3]Peletier L A, Rottsch?fer V. Pattern selection of solutions of the Swift-Hohenberg equation. Physica D, 194:95-126(2004)
[4]Tersian, S., Chaparova, J. Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations.C. R. Math. Acad. Sci. Paris, 331:287-292(2000)
[5]Agarwal, R P. On fourth order boundary value problems arising in beam analysis. Differential Integral Equations, 2(1):91-110(1989)
[6]Webb, J R L., Infante G, Franco D. Positive solutions of nonlinear fourth-order boundary value problems with local and non-local boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A, 138(2):427-446(2008)
[7]Rynne, B P. Infinitely many solutions of superlinear fourth order boundary value problems. Topol.Methods Nonlinear Anal., 19(2):303-312(2002)
[8]Rynne, B P. Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems. J. Differential Equations, 188(2):461-472(2003)
[9]Li Wei, Zhang, Meirong. Non-degeneracy and uniqueness of periodic solutions for some superlinear beam equations. Appl. Math. Lett., 22(3):314-319)
[10]Bai Zhanbing, Wang Haiyan. On positive solutions of some nonlinear fourth-order beam equations.J. Math. Anal. Appl., 270(2):357-368(2002)
[11]Ma Ruyun, Wang Haiyan. On the existence of positive solutions of fourth-order ordinary differential equations. Appl. Anal., 59(14):225-231(1995)
[12]Ma Ruyun. Existence of positive solutions of a fourth-order boundary value problem. Appl. Math.Comput., 168(2):1219-1231(2005)
[13]Ma Ruyun. Nodal solutions for a fourth-order two-point boundary value problem. J. Math. Anal.Appl., 314(1):254-265(2006)
[14]Ma Ruyun. Nodal solutions of boundary value problems of fourth-order ordinary differential equations,J. Math. Anal. Appl., 319(2):424-434(2006)
[15]Ma Ruyun, Thompson B. Nodal solutions for a nonlinear fourth-order eigenvalue problem. Acta Math. Sin.(Engl. Ser.), 24(1):27-34(2008)
[16]Ma Ruyun, Xu Jia. Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem. Nonlinear Anal., 72(1):113-122(2010)
[17]Agarwal R P. Difference Equations and Inequalities.Theory, Methods, and Applications, Second ed.,Monogr. Textbooks Pure Appl. Math., Vol. 228, Marcel Dekker, Inc. New York, 2000
[18]Cabada A, Dimitrov N. Multiplicity results for nonlinear periodic fourth-order difference equations with parameter dependence and singularities. J. Math. Anal. Appl., 371:518-533(2010)
[19]Ma Ruyun, Gao Chenghua, Chang Yongkui. Existence of solutions of a discrete fourth-order boundary value problem, Discrete Dyn. Nat. Soc. 2010, Art. ID 839474, 19 pp.
[20]Ma Ruyun, Xu Youji. Existence of positive solution for nonlinear fourth-order difference equations,Comput. Math. Appl., 59:3770-3777(2010)
[2]Peletier, L A, Rodrígues, J A. Homoclinic orbits to a saddle-center in a fourth-order differential equation. J. Differential Equations, 203:185-215(2004)
[3]Peletier L A, Rottsch?fer V. Pattern selection of solutions of the Swift-Hohenberg equation. Physica D, 194:95-126(2004)
[4]Tersian, S., Chaparova, J. Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations.C. R. Math. Acad. Sci. Paris, 331:287-292(2000)
[5]Agarwal, R P. On fourth order boundary value problems arising in beam analysis. Differential Integral Equations, 2(1):91-110(1989)
[6]Webb, J R L., Infante G, Franco D. Positive solutions of nonlinear fourth-order boundary value problems with local and non-local boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A, 138(2):427-446(2008)
[7]Rynne, B P. Infinitely many solutions of superlinear fourth order boundary value problems. Topol.Methods Nonlinear Anal., 19(2):303-312(2002)
[8]Rynne, B P. Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems. J. Differential Equations, 188(2):461-472(2003)
[9]Li Wei, Zhang, Meirong. Non-degeneracy and uniqueness of periodic solutions for some superlinear beam equations. Appl. Math. Lett., 22(3):314-319)
[10]Bai Zhanbing, Wang Haiyan. On positive solutions of some nonlinear fourth-order beam equations.J. Math. Anal. Appl., 270(2):357-368(2002)
[11]Ma Ruyun, Wang Haiyan. On the existence of positive solutions of fourth-order ordinary differential equations. Appl. Anal., 59(14):225-231(1995)
[12]Ma Ruyun. Existence of positive solutions of a fourth-order boundary value problem. Appl. Math.Comput., 168(2):1219-1231(2005)
[13]Ma Ruyun. Nodal solutions for a fourth-order two-point boundary value problem. J. Math. Anal.Appl., 314(1):254-265(2006)
[14]Ma Ruyun. Nodal solutions of boundary value problems of fourth-order ordinary differential equations,J. Math. Anal. Appl., 319(2):424-434(2006)
[15]Ma Ruyun, Thompson B. Nodal solutions for a nonlinear fourth-order eigenvalue problem. Acta Math. Sin.(Engl. Ser.), 24(1):27-34(2008)
[16]Ma Ruyun, Xu Jia. Bifurcation from interval and positive solutions of a nonlinear fourth-order boundary value problem. Nonlinear Anal., 72(1):113-122(2010)
[17]Agarwal R P. Difference Equations and Inequalities.Theory, Methods, and Applications, Second ed.,Monogr. Textbooks Pure Appl. Math., Vol. 228, Marcel Dekker, Inc. New York, 2000
[18]Cabada A, Dimitrov N. Multiplicity results for nonlinear periodic fourth-order difference equations with parameter dependence and singularities. J. Math. Anal. Appl., 371:518-533(2010)
[19]Ma Ruyun, Gao Chenghua, Chang Yongkui. Existence of solutions of a discrete fourth-order boundary value problem, Discrete Dyn. Nat. Soc. 2010, Art. ID 839474, 19 pp.
[20]Ma Ruyun, Xu Youji. Existence of positive solution for nonlinear fourth-order difference equations,Comput. Math. Appl., 59:3770-3777(2010)