We study the nonlocal equation-ε^ 2 Δ u_ ε+ V u_ ε= ε^-α\bigl (I_ α*| u_ ε|^ p\bigr)| u_ ε|^ p-2
u_ ε\quad in R^ N,-ε 2 Δ u ε+ V u ε= ε-α (I α∗| u ε| p)| u ε| p-2 u ε in RN, where N ≥ 1 N≥ 1, α …

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 …

In this paper we investigate the existence of positive ground state solution for the following
class of elliptic equations where N⩾ 3, V, K are nonnegative continuous functions and f is a …

In this paper we prove the existence of at least three nontrivial solutions for the class of p & q
problems given by− div (a (|∇ u| p)|∇ u| p− 2∇ u)+ V (x) b (| u| p)| u| p− 2 u= K (x) f (u), in …

We study the following nonlinear Choquard equation:-Δ⁢ u+ V⁢(x)⁢ u=(1| x| μ∗ F⁢(u))⁢
f⁢(u) in⁢ ℝ N, where 0< μ< N, N≥ 3, V is a continuous real function and F is the primitive …

In this paper, we study a class of nonlocal Schrödinger-Kirchhoff problems involving only
continuous functions. Using a minimization argument and a quantitative deformation lemma …

We consider the following (p, q)-Laplacian Kirchhoff type problem−(a+ b∫ R 3|∇ u| pdx) Δ
pu−(c+ d∫ R 3|∇ u| qdx) Δ qu+ V (x)(| u| p− 2 u+| u| q− 2 u)= K (x) f (u) in R 3, where a, b, c …

In this paper we prove the existence of a positive and a negative ground state weak solution
for the following class of fractional p&q-Laplacian problems (−∆) s pu+(−∆) s qu+ V (x)(| u| p …

In this paper, we investigate the existence of solutions for the nonlinear Schrödinger–
Poisson system with zero mass. By introducing some new ideas, we prove, via the constraint …

We study the existence and concentration behavior of the bound states for the following
logarithmic Schrödinger equation-ε 2 Δ v+ V (x) v= v log v 2 in RN, v (x)→ 0 as| x|→∞, where …