Existence of nontrivial solutions for the Klein-Gordon-Maxwell system with Berestycki-Lions conditions
Existence of nontrivial solutions for the Klein-Gordon-Maxwell system with Berestycki-Lions conditions
Abstract In this article, we study the following Klein-Gordon-Maxwell system: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mfenced open="{" close=""> <m:mrow> <m:mspace depth="1.25em" /> <m:mtable displaystyle="true"> <m:mtr> <m:mtd columnalign="left"> <m:mo>−</m:mo> <m:mi mathvariant="normal">Δ</m:mi> <m:mi>u</m:mi> <m:mo>−</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mi>ω</m:mi> <m:mo>+</m:mo> <m:mi>ϕ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mi>ϕ</m:mi> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>g</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mo>)</m:mo> …