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<p>The main purpose of this paper is to establish the existence and multiplicity of at least two nontrivial nonnegative weak solutions for a class of quasilinear elliptic systems with nonlinearities of concave–convex type in the context of variable exponent anisotropic Sobolev spaces defined on a bounded domain <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_910_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="116" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Omega \subset {\mathbb {R}}^N (N\ge 3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo>≥</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Our existence theorem for weak solutions is proved by using Nehari manifold decomposition techniques combined with the fibering map analysis of Drabek and Pohozaev (Proc R Soc Edinb Sect A Math 127(4):703–726, 1997) and direct method of calculus of variations.</p>

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Existence and multiplicity of solutions for a class of quasilinear anisotropic elliptic systems via fibering method

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Deepak Kumar Mahanta

摘要

The main purpose of this paper is to establish the existence and multiplicity of at least two nontrivial nonnegative weak solutions for a class of quasilinear elliptic systems with nonlinearities of concave–convex type in the context of variable exponent anisotropic Sobolev spaces defined on a bounded domain \(\Omega \subset {\mathbb {R}}^N (N\ge 3)\) Ω ⊂ R N ( N ≥ 3 ) . Our existence theorem for weak solutions is proved by using Nehari manifold decomposition techniques combined with the fibering map analysis of Drabek and Pohozaev (Proc R Soc Edinb Sect A Math 127(4):703–726, 1997) and direct method of calculus of variations.