Uniqueness of the ground state solutions of quasilinear Schrödinger equations

Soliton Solutions for Quasilinear Schrödinger Equations

Existence and Uniqueness of Solutions of Quasilinear Wave Equations (ii)

In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 o...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

A computer assisted study of uniqueness of ground state solutions

For the problem (here u = u(x)) ∆u− u + αu + βu = 0, x ∈ R, lim |x|→∞ u(x) = 0 , with constants 1 ≤ p < q < r < n+2 n−2 , and α, β > 0, uniqueness of radial solution (called ground state solution) is not known. We present a procedure, which opens the way to produce computer assisted proofs of uniqueness for specific p, q, r, and n.

Uniqueness of ground states for quasilinear elliptic equations in the exponential case

where β is an appropriate positive constant, see [1, 2, 4, 6, 7]. The question of uniqueness of ground states for (1.1) when f(u) has such exponential behavior has not previously been treated; the purpose of this paper is to make a beginning on this problem. Appropriate assumptions on the operator A will be given in the next section. On the other hand, for the nonlinearity f we consider the spe...