Let be a domain in , , . Let and let be a uniformly parabolic operator , , whose coefficients, depending on , are periodic in and satisfy some regularity assumptions. Let be the matrix whose entry is and let be the unit exterior normal to . Let be a -periodic function (that may change sign) defined on whose restriction to belongs to for some large enough . In this paper, we give necessary and sufficient conditions on for the existence of principal eigenvalues for the periodic parabolic Steklov problem on , on , , on . Uniqueness and simplicity of the positive principal eigenvalue is proved and a related maximum principle is given.
T. Godoy. E. Lami Dozo. S. Paczka. "On principal eigenvalues for periodic parabolic Steklov problems." Abstr. Appl. Anal. 7 (8) 401 - 421, 12 September 2002. https://doi.org/10.1155/S1085337502204066