A bifurcation problem for a nonlinear partial differential equation of parabolic type^†

This research was supported by the Office of Naval Research under Contract No. NONR N0014-67-A-0191-0009 and by the United States Air Force Office of Scientific Research (Grant AF-AFOSR-693-67B)

Abstract

We Consider the boundary value problem [d] Here λ is a non negative parameter; f is a given real valuede function defined and a class C² [d] is an arbitrarily specified function of class C¹ on [0, n] satisfying [d] = 0. Under suitable hypotheses concerning f, we investigate the existence and stability properties of stationary solutions for (*). Our approach is to interpret (*) as a dynamical system in an appropriately chosen Banach space, and then to apply to (*) certain known results in the theory of Liapunov stability for general dynamical systems

This research was supported by the Office of Naval Research under Contract No. NONR N0014-67-A-0191-0009 and by the United States Air Force Office of Scientific Research (Grant AF-AFOSR-693-67B)

This research was supported by the Office of Naval Research under Contract No. NONR N0014-67-A-0191-0009 and by the United States Air Force Office of Scientific Research (Grant AF-AFOSR-693-67B)

Notes

This research was supported by the Office of Naval Research under Contract No. NONR N0014-67-A-0191-0009 and by the United States Air Force Office of Scientific Research (Grant AF-AFOSR-693-67B)