Sign-changing solutions for modified nonlinear Schröinger equation

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

Nondegeneracy of Nonradial Sign-changing Solutions to the Nonlinear Schrödinger Equation

We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation ∆u− u + |u|p−1u = 0 in R , u ∈ H(R ) constructed by Musso, Pacard, and Wei [19] are non-degenerate. This provides the first example of a non-degenerate sign-changing solution to the above nonlinear Schrödinger equation with finite energy.

infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

in this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. we use some natural constraints and the ljusternik-schnirelman critical point theory on c1-manifolds, to prove our main results.

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Sign-changing Multi-bump Solutions for Nonlinear Schrödinger Equations with Steep Potential Wells

We study the nonlinear Schrödinger equations: (Pλ) −∆u+(λa(x)+1)u = |u|p−1u, u ∈ H(R ), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|→∞ a(x) ≤ lim sup|x|→∞ a(x) < ∞ and a−1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1 ∪Ω2) and to a presc...