We propose a direct approach for detecting arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms. Although the method works in various frameworks, we illustrate it on the problem ⎪⎨ ⎪⎩ − u+ u=Q(x)[f (u)+ εg(u)], x ∈RN, N 2, u 0, u(x)→ 0 as |x| →∞, (Pε) where Q :RN →R is a radial, positive potential, f : [0,∞)→R is a continuous nonlinearity which oscillates near ...

Abstract In this article, we consider the following quasilinear Schrödinger–Poisson system $$ \textstyle\begin{cases} -\Delta u+V(x)u-u\Delta (u^{2})+K(x)\phi (x)u=g(x,u), \quad x\in \mathbb{R}^{3}, \\ \phi =K(x)u^{2}, \end{cases} { − Δ <mml:mi...

and Applied Analysis 3 In this paper, we also consider themultiplicity of solutions of (7). For each l ∈ Z, let l ∗ u = (u n+lT ) n∈Z , ∀u = (u n ) n∈Z , (21) which defines a Z-action on E. By the periodicity of the coefficients, we know that both J and J󸀠 are Z-invariants. Therefore, ifu ∈ E is a critical point of J, so is l∗u. Two critical points u 1 , u 2 ∈ E of J are said to be geometricall...