Existence of solutions for an impulsive boundary value problem with nonlinear derivative dependence on unbounded intervals via variational methods

Authors

  • Sihem BOUMARAF Laboratory of Fixed Point Theory and Applications, Ecole Normale Sup´erieure, Kouba, Algiers, Algeria, e-mail: boumaraf.sihem@gmail.com
  • Toufik MOUSSAOUI Laboratory of Fixed Point Theory and Applications, Ecole Normale Sup´erieure, Kouba, Algiers, Algeria, e-mail: toufik.moussaoui@gmail.com

DOI:

https://doi.org/10.24193/subbmath.2022.3.05

Keywords:

Impulsive BVPs, unbounded interval, nonlinear derivative dependence, iterative methods, variational methods.

Abstract

In this paper, we employ the critical point theory and iterative methods to establish the existence of solutions for an impulsive boundary value problem with nonlinear derivative dependence on the half-line.

Mathematics Subject Classification (2010): 34B37, 34B40, 35A15, 47J25.

Received 26 October 2019; Accepted 17 January 2020.

References

Badiale, M., Serra, E., Semilinear Elliptic Equations for Beginners. Existence Results via the Variational Approach, Universitext. Springer, London, 2011.

Briki, M., Djebali S., Moussaoui, T., Solvability of an impulsive boundary value problem on the half-line via critical point theory, Bull. Iranian Math. Soc., 43(2017), 601-615.

Chen, H., Sun, J., An application of variational method to second-order impulsive differential equation on the half-line, Appl. Math. Comput., 217(2010), 1863-1869.

De Figueiredo, D., Girardi, M., Matzeu, M., Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques, Differential Integral Equations, 17(2004), 119-126.

Rabinowitz, P.H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, 65. Published for the Conference Board of the Mathematical Sciences, Washington DC; by the American Mathematical Society, Providence, RI, 1986.

Struwe, M., Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 1996.

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Published

2022-09-20

How to Cite

BOUMARAF, S., & MOUSSAOUI, T. (2022). Existence of solutions for an impulsive boundary value problem with nonlinear derivative dependence on unbounded intervals via variational methods. Studia Universitatis Babeș-Bolyai Mathematica, 67(3), 513–531. https://doi.org/10.24193/subbmath.2022.3.05

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