In this paper, we study existence and summability of distributional solutions in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$H_0^1(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$H^1_{\text {loc}}(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mtext>loc</mtext> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> to a class of quasilinear stationary Schrödinger equations with double singularities and a quadratic convection term. The results obtained depend on the summability of a datum g(x) (which belongs to a Lebesgue space) and on a parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> of a singular term. In particular, we establish the existence of distributional solutions in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$H_0^1(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for weak and strongly singular nonlinearities.

On a class of quasilinear elliptic equations with double singularity and quadratic convection term

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2026年7月22日

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Gelson C. G. dos Santos,
Ryan H. Freitas Moura

摘要

In this paper, we study existence and summability of distributional solutions in $H_0^1(\Omega )$ $H_{0}^{1} (Ω)$ or $H^1_{\text {loc}}(\Omega )$ $H_{loc}^{1} (Ω)$ to a class of quasilinear stationary Schrödinger equations with double singularities and a quadratic convection term. The results obtained depend on the summability of a datum g(x) (which belongs to a Lebesgue space) and on a parameter $\lambda $ $λ$ of a singular term. In particular, we establish the existence of distributional solutions in $H_0^1(\Omega )$ $H_{0}^{1} (Ω)$ for weak and strongly singular nonlinearities.