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<p>We investigate the Cauchy problem for <i>p</i>-Laplacian-type equations with an inhomogeneous and nonlinear absorption term, along with initial data <i>kδ</i><sub>0</sub>(<i>x</i>) as <i>k</i> → +<i>∞</i>. We derive sufficient conditions on the parameters of nonlinearity for the existence of very singular solutions, as well as conditions excluding the existence of any singular solution.</p>

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Very singular solutions of p-Laplacian-type equations with spatially inhomogeneous and nonlinear absorption

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Roman M. Taranets

摘要

We investigate the Cauchy problem for p-Laplacian-type equations with an inhomogeneous and nonlinear absorption term, along with initial data kδ0(x) as k → +∞. We derive sufficient conditions on the parameters of nonlinearity for the existence of very singular solutions, as well as conditions excluding the existence of any singular solution.