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<p>In this article, we establish the existence and multiplicity results of weak solutions for a class of quasilinear <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p(x)-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>Laplacian problems with Robin boundary conditions in the generalized Sobolev space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(W^{1,p(x)}(\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>W</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. The main results of this article are derived using the Nehari manifold method under some appropriate assumptions.</p>

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Existence and multiplicity results for a class of \(p(x)-\)Laplacian problems with Robin-type boundary term

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Amar Pal Verma,
  • Rasmita Kar

摘要

In this article, we establish the existence and multiplicity results of weak solutions for a class of quasilinear \(p(x)-\) p ( x ) - Laplacian problems with Robin boundary conditions in the generalized Sobolev space \(W^{1,p(x)}(\Omega )\) W 1 , p ( x ) ( Ω ) . The main results of this article are derived using the Nehari manifold method under some appropriate assumptions.