Research

Research interests

I work in nonlinear analysis applied to partial differential equations. My main focus is the semilinear wave equation under Dirichlet periodic conditions, together with elliptic boundary value problems, singular fourth order ordinary differential equations arising in nanobeam and MEMS models, and delay functional differential equations. I combine topological methods, in particular Leray-Schauder degree theory, with numerical methods such as shooting methods, finite elements, and spectral or FFT techniques.

Older working papers, theses, and course notes, mostly in Spanish, are collected separately on the Trabajos page.

Selected publications

  • Caicedo, J. F., Castro, A., Duque, R., and Sanjuán, A. (2014). Existence of solutions for a semilinear wave equation with non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, Series S, 7(69), pp. 1193 to 1202. Journal link
  • Caicedo, J. F., Castro, A., and Sanjuán, A. (2017). Bifurcation at infinity for a semilinear wave equation. Discrete and Continuous Dynamical Systems, Series A, 37(4), pp. 1857 to 1865. Journal link
  • Caicedo, J. F., Castro, A., Duque, R., and Sanjuán, A. (2017). The semilinear wave equation with non-monotone nonlinearity: a survey. Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 49, pp. 207 to 214. Journal link
  • Pardo, R., and Sanjuán, A. (2020). Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth. Electronic Journal of Differential Equations, 114, pp. 1 to 17. Journal link
  • Amster, P., Epstein, J., and Sanjuán, A. (2021). Periodic solutions for systems of functional differential semilinear equations at resonance. Topological Methods in Nonlinear Analysis, 58(2), pp. 591 to 607. Journal link
  • Caicedo, J. F., Castro, A., Duque, R., and Sanjuán, A. (2023). A semilinear wave equation with non-monotone nonlinearity. Electronic Journal of Differential Equations, Special Issue in Honor of John W. Neuberger, 02, pp. 81 to 86. Journal link
  • Sanjuán, A. (2026). Existence and computation of periodic solutions for the semilinear Gompertz equation with discrete delay. In Proceedings of the Fourth Colombian Conference on Applied and Industrial Mathematics (MAPI 4). Springer. Accepted.
  • Rodriguez, F., and Sanjuán, A. (2026). A system of semilinear wave equations with non-monotone nonlinearity. Dedicated to Professor Alfonso Castro. Submitted to the Electronic Journal of Differential Equations, Special Issue in Honor of Alfonso Castro.

Curriculum vitae

Full CV: download the PDF

Elsewhere