Singular solutions of some elliptic equations involving mixed absorption-reaction
نویسندگان
چکیده
<p style='text-indent:20px;'>We study properties of nonnegative functions satisfying (E)<inline-formula><tex-math id="M1">\begin{document}$ \;-{\Delta} u+u^p-M|\nabla u|^q = 0 $\end{document}</tex-math></inline-formula> in a domain <inline-formula><tex-math id="M2">\begin{document}$ {\mathbb R}^N when id="M3">\begin{document}$ p&gt;1 $\end{document}</tex-math></inline-formula>, id="M4">\begin{document}$ M&gt;0 and id="M5">\begin{document}$ 1&lt;q&lt;p $\end{document}</tex-math></inline-formula>. We concentrate our analysis on the solutions (E) with an isolated singularity, or exterior domain, whole space. The existence such their behaviours depend strongly values exponents id="M6">\begin{document}$ p id="M7">\begin{document}$ q particular according to sign id="M8">\begin{document}$ q-\frac{2p}{p+1} id="M9">\begin{document}$ \frac{2p}{p+1} also value parameter id="M10">\begin{document}$ M which becomes key element. description different is made possible by sharp radial (E).</p>
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022036