| Citation | In the field of non-linear problems in mechanics, Toland is a master of analytical and topological methods who has both added to the abstract theory underlying such methods and applied them to a wide variety of physical problems. He has made fundamental contributions to global bifurcation theory. He discovered a duality principle in the calculus of variations that applies to a class of non-convex functionals and was quite unexpected. He has discovered (with E.N. Dancer) a form of topological degree that allows one to count orbits of specified periods for systems with a first integral. Toland was the first to prove existence of an extreme wave on water, and proceeded (with C.J. Amick) to answer rigorously a number of difficult questions (open for more than a century) in the theory of water waves. He also has definitive results on the stability of rotating chains, on bifurcation for elliptic equations in an infinite strip, on indefinite Hamiltonian systems, and on systems with a plethora of homoclinic orbits. |