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Research Article

Existence of a non-trivial solution for fourth-order elastic beam equations involving Lipschitz non-linearity

| (Reviewing Editor)
Article: 1226040 | Received 08 Jun 2016, Accepted 15 Aug 2016, Published online: 03 Sep 2016

References

  • Afrouzi, G. A., Heidarkhani, S., & O’Regan, D. (2011). Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem. Taiwanese Journal of Mathematics, 15, 201–210.
  • Bai, Z., & Wang, H. (2002). On positive solutions of some nonlinear fourth-order beam equations. Journal of Mathematical Analysis and Applications, 270, 357–368.
  • Bai, Z. (2010). Positive solutions of some nonlocal fourth-order boundary value problem. Applied Mathematics and Computation, 215, 4191–4197.
  • Bonanno, G. (2012). A critical point theorem via the Ekeland variational principle. Nonlinear Analysis, 75, 2992–3007.
  • Bonanno, G., & Di Bella, B. (2008). A boundary value problem for fourth-order elastic beam equations. Journal of Mathematical Analysis and Applications, 343, 1166–1176.
  • Bonanno, G., & Di Bella, B. (2010). A fourth-order boundary value problem for a Sturm-Liouville type equation. Applied Mathematics and Computation, 217, 3635–3640.
  • Bonanno, G., Di Bella, B., & O’Regan, D. (2011). Non-trivial solutions for nonlinear fourth-order elastic beam equations. Computers and Mathematics with Applications, 62, 1862–1869.
  • Busuioc, A., & Ratiu, T. (2003). The second grade fluid and averaged Euler equations with Navier-slip boundary conditions. Nonlinearity, 16, 1119–1149.
  • Cabada, A., Cid, J. A., & Sanchez, L. (2007). Positivity and lower and upper solutions for fourth order boundary value problems. Nonlinear Analysis, 67, 1599–1612.
  • Chai, G. (2007). Existence of positive solutions for fourth-order boundary value problem with variable parameters. Nonlinear Analysis, 66, 870–880.
  • Grossinho, M. R., Sanchez, L., & Tersian, S. A. (2005). On the solvability of a boundary value problem for a fourth-order ordinary differential equation. Applied Mathematics Letters, 18, 439–444.
  • Gyulov, T., & Morosanu, G. (2010). On a class of boundary value problems involving the p-biharmonic operator. Journal of Mathematical Analysis and Applications, 367, 43–57.
  • Han, G., & Xu, Z. (2007). Multiple solutions of some nonlinear fourth-order beam equations. Nonlinear Analysis, 68, 3646–3656.
  • Heidarkhani, S. (2012a). Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouvillie type. Electronic Journal of Differential Equations, 84, 1–15.
  • Heidarkhani, S. (2012b). Non-trivial solutions for a class of p1, ..., pn-biharmonic systems with Navier boundary conditions. Annales Polonici Mathematici, 105, 65–76.
  • Heidarkhani, S. (2014). Existence of non-trivial solutions for systems of n fourth order partial differential equations. Mathematica Slovaca, 645, 1249–1266.
  • Heidarkhani, S., Afrouzi, G. A., Ferrara, M., & Moradi, S. (2016). Variational approaches to impulsive elastic beam equations of Kirchhoff type. Complex Variables and Elliptic Equations. doi:10.1080/17476933.2015.1131681
  • Heidarkhani, S., Ferrara, M., & Khademloo, S. (2016). Nontrivial solutions for one-dimensional fourth-order Kirchhoff-type equations. Mediterranean Journal of Mathematics, 13, 217–236.
  • Heidarkhani, S., Ferrara, M., Salari, A., & Caristi, G. (2016). Multiplicity results for p(x)-biharmonic equations with Navier boundary. Complex Variables and Elliptic Equations, 61, 1494–1516.
  • Khaleghi Moghadam, M., & Heidarkhani, S. (2014). Existence of a Non-trivial solution for nonlinear difference equations. Differential Equations & Applications, 6, 517–525.
  • Khalkhali, S. M., Heidarkhani, S., & Razani, A. (2012). Infinitely many solutions for a fourth-order boundary-value problem. Electronic Journal of Differential Equations, 164, 1–14.
  • Liu, X.-L., & Li, W.-T. (2007a). Existence and multiplicity of solutions for fourth-order boundary values problems with three parameters. Mathematical and Computer Modelling, 46, 525–534.
  • Liu, X.-L., & Li, W.-T. (2007b). Existence and multiplicity of solutions for fourth-order boundary values problems with parameters. Journal of Mathematical Analysis and Applications, 327, 362–375.
  • Li, Y. (2007). On the existence of positive solutions for the bending elastic beam equations. Applied Mathematics and Computation, 189, 821–827.
  • Peletier, L. A., Troy, W. C., & Van der Vorst, R. C. A. M. (1995). Stationary solutions of a fourth order nonlinear diffusion equation. (V. V. Kurt,, Trans.). Differentsialnye Uravneniya (Differential Equations), 31, 301–314.
  • Zeidler, E. (1985). Nonlinear functional analysis and its applications (Vol. II/B). New York, NY: Berlin-Heidelberg.