Nonlinear scalar field equations, I existence of a ground state

A nonlinear elliptic equation with singular potential and applications to nonlinear field equations

“…Indeed, using (14), from Proposition 22 it readily follows that for every m ∈ N \ {0, 1} there exists n m ∈ N such that for any n > n m one can find g 1 , . .…”

“…In ruling out the possibility of a vanishing weak limit, we exploit the growth conditions assumed on f , namely f (t) = O(|t| p−1 ) as t → ∞ and f (t) = O(|t| q−1 ) as t → 0 where p and q are subcritical and supercritical exponents respectively (see hypothesis (f 1 )). Probably these conditions were first considered in [14]. More recently, they have also been used in [5], [9], [10], [11], [12], [29].…”

Soliton solutions for quasilinear Schrödinger equations, I

“…The semilinear case corresponding to κ = 0 has been studied extensively in recent years (e.g., [3], [9], [24]). Quasilinear equations of form (1) appear more naturally in mathematical physics and have been derived as models of several physical phenomena corresponding to various types of h, the superfluid film equation in plasma physics by Kurihara in [13] (cf.…”

Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

“…Our proof is, however, considerably simpler because of radial symmetry. The method used in the existence proof was originally due to Strauss [14] and to Berestycki and Lions [1].…”