Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
Abstract We study the following nonlinear Choquard equation: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mrow> <m:mi>Δ</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>V</m:mi> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>x</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mrow> <m:mfrac> <m:mn>1</m:mn> <m:msup> <m:mrow> <m:mo>|</m:mo> <m:mi>x</m:mi> <m:mo>|</m:mo> </m:mrow> <m:mi>μ</m:mi> …