Multiple Solutions to Neumann Problems with Indefinite Weight and Bounded Nonlinearities
详细信息    查看全文
  • 作者:Alberto Boscaggin ; Maurizio Garrione
  • 关键词:Indefinite weight ; Bounded nonlinearities ; Neumann problem ; Shooting method ; 34B15 ; 34B08
  • 刊名:Journal of Dynamics and Differential Equations
  • 出版年:2016
  • 出版时间:March 2016
  • 年:2016
  • 卷:28
  • 期:1
  • 页码:167-187
  • 全文大小:1,574 KB
  • 参考文献:1.Alama, S., Tarantello, G.: On semilinear elliptic equations with indefinite nonlinearities. Calc. Var. Partial Differ. Equ. 1, 439–475 (1993)CrossRef MathSciNet
    2.Atkinson, F.V., Everitt, W.N., Ong, K.S.: On the \(m\) -coefficient of Weyl for a differential equation with an indefinite weight function. Proc. Lond. Math. Soc. (3) 29, 368–384 (1974)CrossRef MathSciNet
    3.Bandle, C., Pozio, M.A., Tesei, A.: Existence and uniqueness of solutions of nonlinear Neumann problems. Math. Z. 199, 257–278 (1988)CrossRef MathSciNet
    4.Bereanu, C., Mawhin, J.: Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and \(\varphi \) -Laplacian. NoDEA Nonlinear Differential Equ. Appl. 15, 159–168 (2008)CrossRef MathSciNet
    5.Berestycki, H., Capuzzo-Dolcetta, I., Nirenberg, L.: Variational methods for indefinite superlinear homogeneous elliptic problems. NoDEA Nonlinear Differential Equ. Appl. 2, 553–572 (1995)CrossRef MathSciNet
    6.Bonheure, D., Gomes, J.M., Habets, P.: Multiple positive solutions of superlinear elliptic problems with sign-changing weight. J. Differential Equ. 214, 36–64 (2005)CrossRef MathSciNet
    7.Boscaggin, A., Zanolin, F.: Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight. J. Differential Equ. 252, 2900–2921 (2012)CrossRef MathSciNet
    8.Boscaggin, A., Zanolin, F.: Second order ordinary differential equations with indefinite weight: the Neumann boundary value problem. Ann. Mat. Pura Appl. doi:10.​1007/​s10231-013-0384-0
    9.Bravo, J.L., Torres, P.J.: Periodic solutions of a singular equation with indefinite weight. Adv. Nonlinear Stud. 10, 927–938 (2010)MathSciNet
    10.Butler, G.J.: Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations. J. Differential Equ. 22, 467–477 (1976)CrossRef
    11.Cid, J.Á., Sanchez, L.: Periodic solutions for second order differential equations with discontinuous restoring forces. J. Math. Anal. Appl. 288, 349–364 (2003)CrossRef MathSciNet
    12.Feltrin, G., Zanolin, F.: Multiple positive solutions for a superlinear problem: a topological approach, (preprint)
    13.Fonda, A., Garrione, M.: Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions. Adv. Nonlinear Stud. 11, 391–404 (2011)MathSciNet
    14.Gaudenzi, M., Habets, P., Zanolin, F.: An example of a superlinear problem with multiple positive solutions. Atti Sem. Mat. Fis. Univ. Modena 51, 259–272 (2003)MathSciNet
    15.Girão, P.M., Gomes, J.M.: Multibump nodal solutions for an indefinite superlinear elliptic problem. J. Differential Equ. 247, 1001–1012 (2009)CrossRef
    16.Hess, P., Kato, T.: On some linear and nonlinear eigenvalue problems with an indefinite weight function. Comm. Partial Differential Equ. 5, 999–1030 (1980)CrossRef MathSciNet
    17.Le, V.K., Schmitt, K.: Minimization problems for noncoercive functionals subject to constraints. Trans. Am. Math. Soc. 347, 4485–4513 (1995)CrossRef MathSciNet
    18.Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, vol. 74. Springer, New York (1989)CrossRef
    19.Papini, D., Zanolin, F.: A topological approach to superlinear indefinite boundary value problems. Topol. Methods Nonlinear Anal. 15, 203–233 (2000)MathSciNet
    20.Sabatini, M.: On the period function of \(x^{\prime \prime } + f(x)x^{\prime 2} + g(x) = 0\) . J. Differential Equ. 196, 151–168 (2004)CrossRef MathSciNet
    21.Terracini, S., Verzini, G.: Oscillating solutions to second-order ODEs with indefinite superlinear nonlinearities. Nonlinearity 13, 1501–1514 (2000)CrossRef MathSciNet
    22.Ward, J.R.: Periodic solutions of ordinary differential equations with bounded nonlinearities. Topol. Methods Nonlinear Anal. 19, 275–282 (2002)MathSciNet
  • 作者单位:Alberto Boscaggin (1)
    Maurizio Garrione (2)

    1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy
    2. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, 20125, Milano, Italy
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Ordinary Differential Equations
    Partial Differential Equations
    Applications of Mathematics
  • 出版者:Springer Netherlands
  • ISSN:1572-9222
文摘
We study the Neumann boundary value problem for the second order ODE $$\begin{aligned} u^{\prime \prime } + (a^+(t)-\mu a^-(t))g(u) = 0, \qquad t \in [0,T], \end{aligned}$$

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700