Existence of multiple nontrivial solutions for a class of quasilinear Schrödinger equations on $\mathbb{R}^{N}$

Solutions for a class of singular quasilinear equations involving critical growth in R2$\mathbb {R}^2$

“…After this work, several papers have appeared dealing with this class of equations (in the non‐singular case) and new approaches were developed to overcome the difficulties, see for example [3, 4, 8, 43]. In the paper [3], the authors prove an uniqueness result of positive solutions for the problem with $$g(s)$$ being a pure power.…”

“…In [4], the authors treat the problem in dimension $$N=1$$ by considering a more general operator and prove the existence of two solutions for a perturbed problem. In [8, 43], the authors show that the problem has infinitely many solutions by applying the Symmetric Mountain Pass Theorem. We point out that none of the previous papers treats nonlinearities with exponential critical growth.…”

Semiclassical Solutions for a Kind of Coupled Schrödinger Equations

“…So recently, the coupled Schrödinger systems are investigated by the authors [9][10][11][12]. For more related results and physical background on Schrödinger systems, please see [13][14][15][16][17][18][19][20][21][22][23] and references therein.…”

Solutions for quasilinear fourth order elliptic equations on $\mathbb{R}^{N}$ with sign-changing potential

“…The results in [10] were then extended by Cheng-Tang [11]. Another recent paper about the problem (1.1) is Che-Chen [8], where the nonlinearity f (x, u) is sublinear so that the variational functional is coercive. By applying the three critical points theorem from Liu-Su [17] and the classical Clark theorem, multiple solutions are obtained.…”