Nontrivial Solutions of Quasilinear Equations via Nonsmooth Morse Theory

Doubly resonant semilinear elliptic problems via nonsmooth critical point theory

“…On the other hand, we note that Furtado and Silva were mainly concerned with the existence of a nontrivial solution, see [10, Theorem 1.2] (involving further assumptions on g), which is obtained using a Morse theoretic approach in the spirit of [11]. This type of result can probably also be revisited in the light of nonsmooth Morse theory -in that respect, see [4]. After this remark, we conclude the section with a refinement of [ .…”

Three critical points theorem and its application to quasilinear elliptic equations

“…Assume that for some c 0, {u n } ⊂ H 1 0 (Ω) is a (PS) c sequence of I , then by [11,Theorem 3.7] (see also [26,Theorem 2.6] or [21,Proposition 4.5]), it is a (CPS) c sequence.…”

Bounded Positive Critical Points of Some Multiple Integrals of the Calculus of Variations

“…We apply Theorem 2.1 of [2]. Consider Observe that every "I E r is continuous from [0,1] to W~,2(D), so that, by (7) and (8), for every "I E r there exists f E [0,1] such that 1h(f)llw~'2(fl) = R.…”