In this paper, we establish concentration and multiplicity properties of ground state solutions
to the following perturbed double phase problem with competing potentials:-ϵ p Δ pu-ϵ q Δ …

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian Page 1
Proceedings of the Royal Society of Edinburgh, 142A, 1237–1262, 2012 Positive solutions of …

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 …

This paper focuses on the study of multiplicity and concentration phenomena of positive
solutions for the singularly perturbed double phase problem with nonlocal Choquard …

In this paper, we study the following coupled nonlinear Schrödinger system with potentials-ϵ
2 Δ u+ u+ V (x) v= W (x) f (| z|) v in RN,-ϵ 2 Δ v+ v+ V (x) u= W (x) f (| z|) u in RN, where z=(u …

In this paper we concern with the multiplicity and concentration of positive solutions for the
semilinear Kirchhoff type equation where ε> 0 is a small parameter, a, b are positive …

Many problems in science and engineering are described by nonlinear differential
equations, which can be notoriously difficult to solve. Through the interplay of topological …

In this paper we study the existence and concentration behaviors of positive solutions to the
Kirchhoff type equations-ε^ 2 M\left (ε^ 2-N\!\! R^ N| ∇ u|^ 2\, dx\right) Δ u\!+\! V (x) u\!=\! f …

We consider the semilinear equation ε 2 s (− Δ) s u+ V (x) u− up= 0, u> 0, u∈ H 2 s (RN)
where 0< s< 1, 1< p< N+ 2 s N− 2 s, V (x) is a sufficiently smooth potential with inf RV (x)> 0 …

We study a mountain pass characterization of least energy solutions of the following
nonlinear scalar field equation in $\mathbf {R}^ N $:\begin {equation*}-\Delta u= g (u), u\in …