Abstract
In this paper, the existence of solutions for a fourth-order boundary value problem with nonlinear derivative dependence on the half-line is studied which is based on critical point theory and iterative methods.
Similar content being viewed by others
References
Badiale, M., Serra, E.: Semilinear Elliptic Equations for Beginners. Existence results via the variational approach. Universitext. Springer, London (2011)
Brézis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, Berlin (2010)
Briki, M., Moussaoui, T., O’Regan, D.: Existence of solutions for a fourth-order boundary value problem on the half-line via critical point theory. Electron. J. Qual. Theory Differ. Equ. 24, 1–11 (2016)
Enguiça, R., Gavioli, A., Sanchez, L.: Solutions of second-order and fourth-order ODEs on the half-line. Nonlinear Anal. 73, 2968–2979 (2010)
Figueiredo, D.D., Girardi, M., Matzeu, M.: Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques. Differ. Integr. Equ. 17, 119–126 (2004)
Li, F., Zhang, Q., Liang, Z.: Existence and multiplicity of solutions of a kind of fourth-order boundary value problem. Nonlinear Anal. 62, 803–816 (2005)
Liu, X.L., Li, W.T.: Existence and multiplicity of solutions for fourth-order boundary value problems with three parameters. Math. Comput. Model. 46, 525–534 (2007)
Rabinowitz, P.H.: Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, vol. 65. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence (1986)
Struwe, M.: Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. Springer, Berlin (1996)
Teng, K., Zhang, C.: Existence of solution to boundary value problem for impulsive differential equation. Nonlinear Anal. Real World Appl. 11, 4431–4441 (2010)
Yang, Y., Zhang, J.: Existence of infinitely many mountain pass solutions for some fourth-order boundary value problems with a parameter. Nonlinear Anal. 71, 6135–6143 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Boumaraf, S., Moussaoui, T. Existence of Solutions for a Fourth-Order Boundary Value Problem with Nonlinear Derivative Dependence on the Half-Line via Critical Point Theory . Mediterr. J. Math. 16, 140 (2019). https://doi.org/10.1007/s00009-019-1414-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-019-1414-y
Keywords
- Fourth-order BVPs
- unbounded interval
- nonlinear derivative dependence
- iterative methods
- critical point theory