Multiplicity result for a ( <i>p</i> ( <i>x</i> ), <i>q</i> ( <i>x</i> ))-Laplacian-like system with indefinite weights

Abstract

Abstract Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>q</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(p(x),q(x))} Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem ( Appl. Anal. 89 (2010), 1–10).