Existence and Concentration Behavior of Ground State Solutions for a Class of Generalized Quasilinear Schrödinger Equations in ℝN

Localized solutions of higher topological type for semiclassical generalized quasilinear Schrödinger equations

“…For the concentration behavior of solutions in (1.1), Li-Wu [13] studied the existence, multiplicity and concentration of solutions with critical growth by the Ljusternik-Schnirelmann theory. Recently, the existence and concentration behavior of ground state solutions was shown by [3]. To the best of our knowledge, there is no result about multiple localized solutions for (1.1) with asymptotically linear nonlinearity.…”

Ground state solutions for a class of generalized quasilinear Schrödinger‐Maxwell system with critical growth

“…where 𝜆 > 0, and Zhu, Li, and Liang established the existence of ground state solutions for (1.5) when the potential may vanish at infinity and the nonlinear term is subcritical growth. Subsequently, in [14], Chen, Tang, and Cheng obtained the existence of ground state sign-changing solutions via non-Nehari manifold. To the best of our knowledge, there is no work concerning with the existence of ground state solutions for (1.5) with critical growth so far.…”

“…Compared with semilinear elliptic problem (1.6)-(1.10), systems (1.11) and (1.12) are quasilinear elliptic problem and more general than (1.7)- (1.8). In [13,14], authors study the subcritical growth, and we further discuss the existence of ground state solutions with the critical growth. To some extent, Theorems 1.1 and 1.2 are supplement and extension to [13,24,27].…”