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<p>We prove existence of positive solutions <i>u</i> in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W_0^{1,p}(\Omega )\)</EquationSource> </InlineEquation> of the following singular and not coercive nonlinear problem: <Equation ID="Equa"> <EquationSource Format="TEX">\( \left\{ \begin{array}{cl} -\textrm{div}\Big ( \frac{\Phi (x,\nabla u)}{u^{\theta \,(p-1)}} \Big ) = f(x) &amp; \hbox {in }\Omega , \\ u &gt; 0 &amp; \hbox {in }\Omega , \\ u = 0 &amp; \hbox {on }\partial \Omega . \\ \end{array} \right. \)</EquationSource> </Equation></p>

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Existence of solutions for singular not coercive nonlinear elliptic equations

  • 期刊论文

  • 发表日期：

    2025年10月8日

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  • Lucio Boccardo,
  • Luigi Orsina

摘要

We prove existence of positive solutions u in \(W_0^{1,p}(\Omega )\) of the following singular and not coercive nonlinear problem: \( \left\{ \begin{array}{cl} -\textrm{div}\Big ( \frac{\Phi (x,\nabla u)}{u^{\theta \,(p-1)}} \Big ) = f(x) & \hbox {in }\Omega , \\ u > 0 & \hbox {in }\Omega , \\ u = 0 & \hbox {on }\partial \Omega . \\ \end{array} \right. \)