Nonsmooth critical point theorems and its applications to quasilinear schrödinger equations

Infinitely many solutions to a quasilinear Schrödinger equation with a local sublinear term

“…Consequently, the standard critical point theory can not be applied directly. In order to overcome this difficulty, several approaches have been successfully developed in the last decade, such as the constraint minimization ( [29]), the Nehari manifold method ( [27]), the perturbation method ( [32]) and the nonsmooth critical point theory ( [6,22]). It seems that the first contribution to the equation (1.1) via variational methods dues to the work [11].…”

Concentration behavior of ground states for a generalized quasilinear Choquard equation

“…The quasilinear Schrödinger Equation (1) is derived as models of several physical phenomenas, see, for example, previous studies. [1][2][3][4] To our best knowledge, the first work to study Equation (1) on mathematics can date back to de Bouard et al 5 Ever since then, there are many works focus on the existence, multiplicity, and concentration of (1), we can refer to previous studies [6][7][8][9][10][11][12][13][14][15] for the subcritical case and to previous studies [16][17][18][19][20][21] for the critical case, respectively. Equation (2) also can be used to describe many physical models.…”