Fourth order ordinary differential operators with general Wentzell boundary conditions

Authors

Angelo Favini, Alma Mater Studiorum Università di BolognaFollow
Gisèle Ruiz Goldstein, University of MemphisFollow
Jerome A. Goldstein, University of MemphisFollow
Silvia Romanelli, Università degli studi di Bari Aldo Moro

Abstract

We consider the fourth order ordinary differential operator Au:= (au″)″ with boundary conditions (eqution found) and one of uʹ(j); u″(j) vanishes for j = 0, 1: Here β0 < 0 < β1: Then A is essentially selfadjoint and bounded below on the Hilbert space H = L2(0, 1) ⊕ C2w, the completion of C[0, 1] under the inner product (eqution found) where wj:= (–1)j+1/Bj for j = 0, 1. Applications to partial differential equations are given.

Publication Title

Differential Equations: Inverse and Direct Problems

Recommended Citation

Favini, A., Goldstein, G., Goldstein, J., & Romanelli, S. (2006). Fourth order ordinary differential operators with general Wentzell boundary conditions. Differential Equations: Inverse and Direct Problems, 59-72. Retrieved from https://digitalcommons.memphis.edu/facpubs/4698