Morse theory by perturbation methods with applications to harmonic maps

K. Uhlenbeck
1981 Transactions of the American Mathematical Society  
There are many interesting variational problems for which the Palais-Smale condition cannot be verified. In cases where the Palais-Smale condition can be verified for an approximating integral, and the critical points converge, a Morse theory is valid. This theory applies to a class of variational problems consisting of the energy integral for harmonic maps with a lower order potential.
doi:10.1090/s0002-9947-1981-0626490-x fatcat:dbrtunjg4ncjfarjrr3o62vxgy