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In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a  p x -Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new  p x -Kirchhoff problem has at least two nontrivial weak solutions.

journal of function spaces

The Multiplicity of Nontrivial Solutions for a New <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>p</mi> <mfenced open="(" close=")"> <mrow> <mi>x</mi> </mrow> </mfenced> </math>-Kirchhoff-Type Elliptic Problem

The Multiplicity of Nontrivial Solutions for a New p x -Kirchhoff-Type Elliptic Problem

The Multiplicity of Nontrivial Solutions for a New $p (x)$ -Kirchhoff-Type Elliptic Problem