We study the existence, multiplicity and concentration behavior of positive solutions for the
nonlinear Kirchhoff type problem where ε> 0 is a parameter and a, b> 0 are constants; V is a …

In this paper, we study the following nonlinear problem of Kirchhoff type with pure power
nonlinearities:(0.1){−(a+ b∫ R 3| D u| 2) Δ u+ V (x) u=| u| p− 1 u, x∈ R 3, u∈ H 1 (R 3), u> 0 …

In this paper we study the existence of normalized solutions to the following nonlinear
Schrödinger equation with critical growth-Δ u= λ u+ f (u), in RN, u> 0,∫ RN| u| 2 dx= a 2 …

In this paper we study the semiclassical limit for the singularly perturbed Choquard
equation− ε 2 Δ u+ V (x) u= ε μ− 3 (∫ R 3 Q (y) G (u (y))| x− y| μ dy) Q (x) g (u) in R 3, where …

The aim of this book is to collect a set of results concerning nonlinear Schrödinger equations
in the whole space driven by fractional operators. The material presented here was mainly …

We study the following singularly perturbed nonlocal Schrödinger equation− ε 2 Δ u+ V (x)
u= ε μ− 2 [1| x| μ⁎ F (u)] f (u) in R 2, where V (x) is a continuous real function on R 2, F (s) is …

Abstract Let G=(V, E) be a locally finite graph, whose measure μ (x) has positive lower
bound, and Δ be the usual graph Laplacian. Applying the mountain-pass theorem due to …

In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The
nonlinearity of the equation is assumed to have exponential growth or have critical growth in …

In this paper, we study the semilinear elliptic equation− Δ u+ a (x)| u| p− 2 u− b (x)| u| q− 2 u=
0 on a Cayley graph of a discrete group of polynomial growth with the homogeneous …

In this paper, we study the existence of solutions with prescribed L2‐norm for the following
Kirchhoff type equation: where N≤ 3, a, b> 0 are constants, p∈(2, 2*), 2*= 6 if N= 3, and …