Monotone heteroclinic solutions to semilinear PDEs in cylinders and applications Regibus, Fabio De Ruiz Aguilar, David In this paper we show the existence of strictly monotone heteroclinic type solutions of semilinear elliptic equations in cylinders. The motivation of this construction is twofold: first, it implies the existence of an entire bounded solution of a semilinear equation without critical points which is not one-dimensional. Second, this gives an example of a bounded stationary solution for the 2D Euler equations without stagnation points which is not a shear flow, completing previous results of Hamel and Nadirashvili. The proof uses a minimization technique together with a truncation argument, and a limit procedure. 2025-05-02T07:56:13Z 2025-05-02T07:56:13Z 2025-03-24 journal article De Regibus, F., Ruiz, D. Monotone heteroclinic solutions to semilinear PDEs in cylinders and applications. Calc. Var. 64, 111 (2025). [https://doi.org/10.1007/s00526-025-02975-x] https://hdl.handle.net/10481/103881 10.1007/s00526-025-02975-x eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature