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<p>We consider a nonlinear elliptic Dirichlet problem driven by a nonhomogeneous differential operator. In the reaction, we have the combined effects of a parametric singular term plus a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((p-1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-superlinear perturbation. We do not assume that the perturbation is positive, not even locally at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>0</mn> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>. This is in sharp contrast to all previous works in the literature. We prove an existence and multiplicity theorem which is global in the parameter (a bifurcation-type theorem).</p>

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Nonhomogeneous singular problems with sign-changing perturbation

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Eylem Öztürk,
  • Nikolaos S. Papageorgiou

摘要

We consider a nonlinear elliptic Dirichlet problem driven by a nonhomogeneous differential operator. In the reaction, we have the combined effects of a parametric singular term plus a \((p-1)\) ( p - 1 ) -superlinear perturbation. We do not assume that the perturbation is positive, not even locally at \(0^+\) 0 + . This is in sharp contrast to all previous works in the literature. We prove an existence and multiplicity theorem which is global in the parameter (a bifurcation-type theorem).