Nonlinear scalar multipoint boundary value problems at resonance

References

• L. Cesari and R. Kannan, An abstract existence theorem at resonance, Proc. Amer. Math. Soc 63 (1977), pp. 221–225. doi: 10.1090/S0002-9939-1977-0448180-3
   Web of Science ®Google Scholar
• S. Chow and J.K. Hale, Methods of Bifurcation Theory, Springer, Berlin, 1982.
   Google Scholar
• P. Drábek, On the resonance problem with nonlinearity which has arbitrary linear growth, J. Math. Anal. Appl. 127 (1987), pp. 435–442. doi: 10.1016/0022-247X(87)90121-1
   Web of Science ®Google Scholar
• P. Drábek, Landesman-Lazer type condition and nonlinearities with linear growth, Czechoslovak Math. J. 40 (1990), pp. 70–86.
   Web of Science ®Google Scholar
• S. Elaydi, An Introduction to Difference Equations, Springer, New York, 2005.
   Google Scholar
• D.L. Etheridge and J. Rodríguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996), pp. 119–137. doi: 10.1080/00036819608840473
   Google Scholar
• R.E. Gaines and J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Mathematics, Springer-Verlag, 1977.
   Google Scholar
• Z. Guo, Z. Zhou, and J. Yu, Periodic solutions of higher-dimensional discrete systems, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), pp. 1013–1022. doi: 10.1017/S0308210500003553
   Google Scholar
• J. Henderson and R. Luca, Positive solutions for a system of second-order multi-point discrete boundary value problems, J. Difference Equ. Appl. 18(9) (2012), pp. 1575–1592. doi: 10.1080/10236198.2011.582868
   Web of Science ®Google Scholar
• J. Henderson and H.B. Thompson, Existence of multiple solutions for second-order discrete boundary value problems, Comput. Math. Appl. 43(10–11) (2002), pp. 1239–1248. doi: 10.1016/S0898-1221(02)00095-0
   Web of Science ®Google Scholar
• J. Henderson, S.K. Ntouyas, and I.K. Purnaras, Positive solutions for systems of three-point nonlinear discrete boundary value problems, Neural Parallel Sci. Comput. 16 (2008), pp. 209–223.
   Google Scholar
• J. Henderson, S.K. Ntouyas, and I.K. Purnaras, Positive solutions for systems of nonlinear discrete boundary value problems, J. Difference Equ. Appl. 15(10) (2009), pp. 895–912. doi: 10.1080/10236190802350649
   Web of Science ®Google Scholar
• R. Iannacci and M.N. Nkashama, Nonlinear two point boundary value problems without Landesman-Lazer condition, Proc. Amer. Math. Soc. 106 (1989), pp. 943–952.
   Web of Science ®Google Scholar
• W. Jiang, B. Wang, and Z. Wang, Solvability of a second-order multi-point boundary-value problems at resonance on a half-line with dimkerL=2, Electron. J. Differential Equations 2011(120) (2011), pp. 1–11.
   Google Scholar
• W.G. Kelley and A.C. Peterson, Difference Equations, Academic Press, New York, 1978.
   Google Scholar
• E.M. Landesman and A.C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1969), pp. 609–623.
   Google Scholar
• A.C. Lazer and D.F. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Mat. Pure Appl. 82 (1969), pp. 49–68. doi: 10.1007/BF02410787
   Google Scholar
• R. Ma, Nonlinear discrete sturm-liouville problems at resonance, Nonlinear Anal. 67 (2007), pp. 3050–3057. doi: 10.1016/j.na.2006.09.058
   Web of Science ®Google Scholar
• D. Maroncelli, Scalar multi-point boundary value problems at resonance, Differ. Equ. Appl. 7(4) (2015), pp. 449–468.
   Web of Science ®Google Scholar
• D. Maroncelli and J. Rodríguez, On the solvability of multipoint boundary value problems for discrete systems at resonance, J. Difference Equ. Appl. 20 (2013), pp. 24–35. doi: 10.1080/10236198.2013.805216
   Web of Science ®Google Scholar
• D. Maroncelli and J. Rodríguez, Existence theory for nonlinear Sturm-Liouville problems with unbounded nonlinearities, Differ. Eqn. Appl. 6(4) (2014), pp. 455–466.
   Google Scholar
• D. Maroncelli and J. Rodríguez, On the solvability of nonlinear impulsive boundary value problems, Topol. Methods Nonlinear Anal. 44(2) (2014), pp. 381–398. doi: 10.12775/TMNA.2014.052
   Web of Science ®Google Scholar
• D. Maroncelli and J. Rodríguez, Periodic behaviour of nonlinear, second-order, discrete dynamical systems, J. Difference Equ. Appl. 22(2) (2015), pp. 280–294. doi: 10.1080/10236198.2015.1083016
   Web of Science ®Google Scholar
• D. Pollack and P. Taylor, Multipoint boundary value problems for discrete nonlinear systems at resonance, Int. J. Pure Appl. Math. 63 (2010), pp. 311–326.
   Google Scholar
• J. Rodríguez, An alternative method for boundary vallue problems with large nolinearities, J. Differential Equations 43 (1982), pp. 157–167. doi: 10.1016/0022-0396(82)90088-2
   Web of Science ®Google Scholar
• J. Rodríguez, Galerkin's method for ordinary differential equations subject to generalized nonlinear boundary conditions, J. Differential Equations 97 (1992), pp. 112–126. doi: 10.1016/0022-0396(92)90086-3
   Web of Science ®Google Scholar
• J. Rodríguez, Nonlinear discrete Sturm-Liouville problems, J. Math. Anal. Appl. 308(1) (2005), pp. 380–391. doi: 10.1016/j.jmaa.2005.01.032
   Web of Science ®Google Scholar
• J.F. Rodríguez, Existence theory for nonlinear eigenvalue problems, Appl. Anal. 87(3) (2008), pp. 293–301. doi: 10.1080/00036810801911280
   Web of Science ®Google Scholar
• J. Rodríguez and Z. Abernathy, Nonlinear discrete Sturm-Liouville problems with global boundary conditions, J. Difference Equ. Appl. 18 (2012), pp. 431–445. doi: 10.1080/10236198.2010.505237
   Web of Science ®Google Scholar
• J. Rodríguez and D.L. Etheridge, Periodic solutions of nonlinear second-order difference equations, Adv. Difference Eqn. 2005 (2) (2005), pp. 173–192.
   Google Scholar
• J. Rodríguez and D. Sweet, Projection methods for nonlinear boundary value problems, J. Differential Equations 58 (1985), pp. 282–293. doi: 10.1016/0022-0396(85)90017-8
   Web of Science ®Google Scholar
• J. Rodríguez and P. Taylor, Scalar discrete nonlinear multipoint boundary value problems, J. Math. Anal. Appl. 330 (2007), pp. 876–890. doi: 10.1016/j.jmaa.2006.08.008
   Web of Science ®Google Scholar
• J. Rodríguez and P. Taylor, Weakly nonlinear discrete multipoint boundary value problems, J. Math. Anal. Appl. 329 (2007), pp. 77–91. doi: 10.1016/j.jmaa.2006.06.024
   Web of Science ®Google Scholar
• J. Rodríguez and P. Taylor, Multipoint boundary value problems for nonlinear ordinary differential equations, Nonlinear Anal. 68 (2008), pp. 3465–3474. doi: 10.1016/j.na.2007.03.038
   Web of Science ®Google Scholar
• N. Rouche and J. Mawhin, Ordinary Differential Equations, Pitman, London, 1980.
   Google Scholar
• S. Wang, J. Liu, and J. Zhang, Multiple solutions for boundary value problems of second order difference equations with resonance, J. Math. Anal. Appl. 374 (2011), pp. 187–196. doi: 10.1016/j.jmaa.2010.09.025
   Web of Science ®Google Scholar
• G. Zhang and R. Medina, Three-point boundary value problems for difference equations, Comput. Math. Appl. 48 (2004), pp. 1791–1799. doi: 10.1016/j.camwa.2004.09.002
   Web of Science ®Google Scholar
• Z. Zhao and J. Liang, Existence of solutions to functional boundary value problems of second-order nonlinear differential equations, J. Math. Anal. Appl. 373 (2011), pp. 614–634. doi: 10.1016/j.jmaa.2010.08.011
   Web of Science ®Google Scholar