Multiple solutions for a parametric Steklov problem involving the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>p</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>x</a:mi> <a:mo stretchy="false">)</a:mo></a:math>-Laplacian operator

In this paper, we study the existence and multiplicity of weak solutions for a Steklov problem involving <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>p</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>x</a:mi> <a:mo stretchy="false">)</a:mo> </a:math>-Laplacian operator in a bounded domain <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi mathvariant="normal">Ω</d:mi> <d:mo>⊂</d:mo> <d:msup> <d:mrow class="MJX-TeXAtom-ORD"> <d:mi mathvariant="double-struck">R</d:mi> </d:mrow> <d:mi>N</d:mi> </d:msup> <d:mtext> </d:mtext> <d:mo stretchy="false">(</d:mo> <d:mi>N</d:mi> <d:mo>≥</d:mo> <d:mn>2</d:mn> <d:mo stretchy="false">)</d:mo> </d:math> with smooth boundary <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi mathvariant="normal">∂</j:mi> <j:mi mathvariant="normal">Ω</j:mi> </j:math>. The boundary equation is perturbed with some weight functions belonging to approriate generalized Lebesgue spaces and two real parameters. Our arguments are based on variational method, using "Mountain Pass Theorem", "Fountain Theorem" and "Dual Fountain Theorem" combined with the critical points theory, we prove several existence results.