Resumen de Quasilinear Schrödinger Equations with Stein–Weiss Type Nonlinearity and Potential Vanishing at Infinity
In this paper, we consider the following quasilinear Schrödinger equation involving Stein–Weiss type nonlinearity:
−u + V(x)u − (u2)u = 1 |x| α RN G(u(y)) |y − x| μ|y| α dy g(u(x)), in RN , where N ≥ 3, 0 <μ< N, α ≥ 0 and 2α + μ < min{ N+2 2 , 4} and G is the primitive of function g. The potential V : RN → R may decay to zero at infinity. By using variational methods, penalization technique and L∞-estimates, we obtain the existence of a positive solution for the above quasilinear Schrödinger equation.
