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 …

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 …

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 …

A celebrated conjecture due to De Giorgi states that any bounded solution of the equation
Δu+(1–u²) u= 0 in ℝ N with∂ yN u> 0 must be such that its level sets u–λ are all …

This introduction to the singularly perturbed methods in the nonlinear elliptic partial
differential equations emphasises the existence and local uniqueness of solutions exhibiting …

The Ohta–Kawasaki density functional theory of diblock copolymers gives rise to a nonlocal
free boundary problem. In a proper range of the block composition parameter and the …

We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the
sphere S^ 2 S 2, u_t&= Δ u+| ∇ u|^ 2 u\quad in Ω * (0, T)\u&= φ\quad on ∂ Ω * (0, T)\u (⋅, 0) …

Green’s function and infinite-time bubbling in the critical nonlinear heat equation Page 1 DOI
10.4171/JEMS/922 J. Eur. Math. Soc. 22, 283–344 c European Mathematical Society 2020 …

We construct a new class of entire solutions for the Allen–Cahn equation Δu+ (1− u2) u= 0,
in R2 (∼ C). Given k⩾ 1, we find a family of solutions whose zero level sets are, away from a …