Regular solutions of elliptic boundary-value problems with discontinuous nonlinearities
M. G. Lepchinskiĭ, Vyacheslav Nikolaevich Pavlenko · St Petersburg Mathematical Journal · 2006
The existence of stable solutions to elliptic boundary-value problems is studied; stability is understood with respect to perturbations of nonlinearities. By the variational method, it is shown that stable solutions of such problems do exist provided a certain integral measure of closeness for (possibly, discontinuous) nonlinearities is employed. It is shown that problems with discontinuous nonlinearities can serve as idealization of problems with continuous nonlinearities but having narrow regions of ill-controlled variations with respect to the phase variable.