Prefer a chat interface with context about you and your work?
Multiple Solutions for Elliptic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>p</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math>-Kirchhoff-Type Potential Systems …
In this paper, we establish the existence of at least three weak solutions for a parametric double eigenvalue quasi-linear elliptic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>p</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:math>-Kirchhoff-type potential system. Our approach is based on a variational method, and a three critical point theorem is obtained by …