Infinitely many small solutions for a modified nonlinear Schrödinger equations

Multiple Solutions of Sublinear Quasilinear Schrödinger Equations with Small Perturbations

“…[6, 7, 9, 15-18, 20, 23]. When g(x, t) is odd in t and h ≡ 0, (1.1) possesses a natural Z 2 symmetry, and some results of multiple solutions for quasilinear Schrödinger equations in bounded domains or whole space have been obtained with g satisfying various conditions, see [14,25,26,32,33] and the references therein. It is worth pointing out that the Z 2 symmetry plays a crucial part in these works.…”

Existence and nonexistence of ground states for a class of quasilinear Schrödinger equations

“…The problem (1.2) has been widely investigated. For example, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Especially, the study of ground states has made great progress and attracted many authors' attention for its great physical interests.…”

Multiplicity of Solutions for a Modified Schrödinger-Kirchhoff-Type Equation in RN

“…Equations (5) are derived as model of several physical phenomena, such as [9,10]. Many achievements had been obtained on the existence of ground states, infinitely many solutions, and soliton solutions for (4), by a dual approach, Nehari method, and the minimax methods in critical point theory, applying the perturbation approach and the Lusternik-Schnirelmann category theory; see [11][12][13][14][15][16][17][18].…”