Multibump solutions for quasilinear elliptic equations with critical growth

Abstract

The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrödinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217-1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040-4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct multibump bound state solutions. C 2013 AIP Publishing LLC.

Ground state solutions for a modified fractional Schrödinger equation with critical exponent

“…Equation 6 has been extensively studied in recent years, for example, see literature. [15][16][17][18][19][20][21][22][23][24][25][26][27][28] But, as 0 < < 1, a few results are seen for Equation (1) (see Li and Wu 29 ).…”

“…Equation is called modified nonlinear Schrödinger equation, which arises in several models of different physical phenomena, such as in the study of superfluid films in plasma physics and in condensed matter theory. Equation has been extensively studied in recent years, for example, see literature . But, as , a few results are seen for Equation (see Li and Wu).…”