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 …

We investigate nonlinear Schrödinger equations like the model equation where the potential
Vλ has a potential well with bottom independent of the parameter λ> 0. If λ→∞ the infimum …

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 …

Diffusion, Cross-Diffusion, and Their Spike-Layer Steady States Page 1 JANUARY 1998
NOTICES OF THE AMS 9 Diffusion, Cross-Diffusion, and Their Spike-Layer Steady States …

This Research Note addresses several pivotal problems in spectral theory and nonlinear
functional analysis in connection with the analysis of the structure set of zeroes of a general …

This paper is concerned with the existence and qualitative property of standing wave
solutions for the nonlinear Schrödinger equation with E being a critical frequency in the …

We consider existence and asymptotic behavior of solutions for an equation of the formε
2Δu− V (x) u+ f (u)= 0, u> 0, u∈ H 10 (Δ),((*)) whereΔis a smooth domain in RN, not …

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 …

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 …