Soliton solutions for quasilinear Schrödinger equations, II

MULTIPLE SOLUTIONS FOR A CLASS OF QUASILINEAR SCHRÖDINGER SYSTEM IN ℝN

“…(1.3) has received great interest and there are recent mathematical studies in the existence of solutions for (1.3). Among others we refer to [6,7,11,13] and the references therein.…”

Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Elliptic Equations in <b><i>R</i></b>²

“…ÀDu À kDðjuj a Þjuj aÀ2 u ¼ gðuÞ in R N : ð1:3Þ (see [1], [2], [5], [10], [11], [17], [18], [21], [22]). Particularly it has been shown that the uniqueness and non-degeneracy of the ground state holds for any k > 0 when N ¼ 1 (see [5], [11]).…”

Multiple Solutions for Quasilinear Elliptic Equations With Critical Growth

“…α and β are real parameters. We believe that 2(p * ) is the critical growth for problem (1.2), since when p = 2 whose critical exponent is 2(2 * ) (see [10,14,19]). …”

“…Equations with more general dissipative term arise in plasma physics, fluid mechanics, in the theory of Heisenberg ferromagnets, etc. For further physical motivations and a more complete list of references dealing with application, we refer to [9,10,11] and references therein. In [16], the existence of positive ground state solutions for the quasilinear Schrödinger equation…”

“…For the case of subcritical growth, the equation (1.3) were studied by a number of authors. In [10], by a change of variables the quasilinear problem was transformed to a semilinear one and an Orlicz space was used as the working space, and they were able to prove the existence of positive solutions by using the Mountain-pass Theorem. The same method of changing of variables was used in [5], but the usual Sobolev space H 1 (R N ) was used as the working space and they proved the existence of a spherically symmetric solution from the classical results given by H. Berestycki and P. L. Lions [8].…”