Existence and multiplicity of radial sign-changing solutions for the Schrödinger–Born–Infeld system

This paper is concerned with the existence and multiplicity of radial sign-changing solutions for a Schrödinger–Born–Infeld system in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msup> <a:mrow class="MJX-TeXAtom-ORD"> <a:mi mathvariant="double-struck">R</a:mi> </a:mrow> <a:mn>3</a:mn> </a:msup> </a:math> , involving a general subcritical nonlinearity <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>f</d:mi> <d:mo stretchy="false">(</d:mo> <d:mi>u</d:mi> <d:mo stretchy="false">)</d:mo> </d:math> . By employing variational methods, specifically the method of invariant sets of a descending flow, we establish the existence of at least one such solution under a general set of assumptions on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi>f</g:mi> </g:math> . Furthermore, when the nonlinearity <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>f</h:mi> </h:math> is odd, we prove that the system admits a sequence of radial sign-changing solutions whose energies are unbounded.