Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight
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DOI: 10.1007/s10440-020-00347-5
Abstract: Let $p>0$ and $(-\Delta )^{s}$ is the fractional Laplacian with $0< s2s$ and $h$ is a nonnegative, continuous function satisfying $h(x)\geq C|x|^{a}$ , $a\geq 0$ , when $|x|$ large. We prove the nonexistence of positive… read more here.
Keywords: solutions fractional; fractional singular; elliptic equation; equation weight ... See more keywords
On certain degenerate and singular elliptic PDEs I: Nondivergence form operators with unbounded drifts and applications to subelliptic equations
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DOI: 10.1016/j.jde.2017.09.017
Abstract: Abstract We prove a Harnack inequality for nonnegative strong solutions to degenerate and singular elliptic PDEs modeled after certain convex functions and in the presence of unbounded drifts. Our main theorem extends the Harnack inequality… read more here.
Keywords: elliptic pdes; nondivergence form; degenerate singular; unbounded drifts ... See more keywords
Singular elliptic equations with quadratic gradient term
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125245
Abstract: Abstract We establish the existence of a non-trivial weak solution to the following singular quasilinear equation with Hardy potential and singular quadratic gradient term: { − Δ u − μ u | x | 2… read more here.
Keywords: quadratic gradient; gradient term; elliptic equations; singular elliptic ... See more keywords
Singular elliptic problems with unbalanced growth and critical exponent
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DOI: 10.1088/1361-6544/ab81ed
Abstract: In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1}, \ u>0, \ \text{ in } \Om \\… read more here.
Keywords: unbalanced growth; critical exponent; growth critical; problems unbalanced ... See more keywords