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<p>We consider a singular Dirichlet problem driven by a variable unbalanced growth differential operator and a singular reaction with an unbounded coefficient and an exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta \in C(\overline{\Omega })\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>∈</mo> <mi>C</mi> <mo stretchy="false">(</mo> <mover> <mi mathvariant="normal">Ω</mi> <mo>¯</mo> </mover> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> which is less than&#xa0;1 only near <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\partial \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation>. Using approximations, we show that the problem has a&#xa0;unique bounded solution.</p>

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Singular elliptic equations with (p(z), q(z))-growth

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Witold Majdak,
  • Nikolaos S. Papageorgiou

摘要

We consider a singular Dirichlet problem driven by a variable unbalanced growth differential operator and a singular reaction with an unbounded coefficient and an exponent \(\eta \in C(\overline{\Omega })\) η ∈ C ( Ω ¯ ) which is less than 1 only near \(\partial \Omega \) ∂ Ω . Using approximations, we show that the problem has a unique bounded solution.