Periodic solutions for the coupled wave equations with concave-convex nonlinearities

In this work, we show that the coupled wave equations possess infinitely many time-periodic solutions. The nonlinearities are the combination of a convex term and a concave term, and we mainly focus on the effect of the concave term on the solution structure of the periodic-Dirichlet wave equations. The proof is based on the detailed analysis for the spectrum structure of the corresponding linear operator, and we obtain the existence and multiplicity of time-periodic solutions to our problem by critical point theory and approximation arguments. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.