Second Existence Theorem for a Class of Variational Equations with Non-Coercive Main Part

Abstract

By using “the fibering idea”, we have established a second existence theorem for the equation ∂A(u) = ∑ j=1 m [∂D j (u)] where A (main part) and D j are non-negative functionals defined in a real and reflexive Banach space and they fulfill certain conditions with A non-coercive and ∂ is the Frechet differential operator. Moreover, we analyze this equation in some concrete cases.