Positive solutions of quasilinear Schrödinger equations with critical growth

Abstract

a b s t r a c tWe consider a class of quasilinear Schrödinger equations of the formWhen 3 < p < 22 * − 1, some existence results have been established by several authors in recent years. Here we are interested in the case that 1 < p ≤ 3. The existence of positive solutions is proved by the variational method. Both well potentials and periodic ones are considered.

Infinite many Blow-up solutions for a Schrödinger quasilinear elliptic problem with a non-square diffusion term

“…Coming back to problem (1.1), we note that issues about existence and multiplicity of solutions for equations related to the equation in (1.1) (since positive, negative to nodal solutions) have been treated by a number of researchers recently, but there is no accurate results for existence of solutions to (1.1), that is, with the blow up behavior for the solutions. See for instance [12,20,5,2,18,19,22] and references therein.…”

Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents

“…Moreover, Zeng, Zhang and Zhou [30] studied the positive solutions of a quasilinear Schrödinger equation with Hardy potential and critical exponent. For more information about change of variable approach, we refer to [13,24,29,8,26,14] and references therein. However, this method depends heavily on the special structure of the quasilinear term and can not be generalized to treating more general quasilinear problems.…”