Radial Symmetry of Entire Solutions of a Biharmonic Equation with Supercritical Exponent
Advanced Nonlinear Studies, 2019 Necessary and sufficient conditions for a regular positive entire solution u of a biharmonic ...
Guo Zongming, Wei Long
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Existence of entire solutions for singular quasilinear convective elliptic systems [PDF]
arXiv, 2021 The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is first solved. Then, a priori estimates, fixed point arguments, nonlinear regularity, compactness results concerning ...
arxiv
Strongly singular convective elliptic equations in RN driven by a non-homogeneous operator [PDF]
arXiv, 2021 Existence of a generalized solution to a strongly singular convective elliptic equation in the whole space is established. The differential operator, patterned after the (p,q)-Laplacian, can be non-homogeneous. The result is obtained by solving some regularized problems through fixed point theory, variational methods and compactness results, besides ...
arxiv
Advances in Nonlinear AnalysisWe prove an existence result for a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction.
Baldelli Laura, Guarnotta Umberto
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On removable singular sets for solutions of higher order differential inequalities [PDF]
arXiv, 2022 We obtain conditions guaranteeing that weak solutions of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge f (x) g (|u|) \quad \mbox{in } \Omega \setminus S, $$ has a removable singular set $S \subset \Omega$, where $\Omega$ is a bounded domain and $a_\alpha$, $f$, and $g$ are some functions.
arxiv
On the classification of entire solutions to the critical p-Laplace equation [PDF]
arXiv, 2022 Under the assumption of finite energy, positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$ for $1< p
arxiv
Nondegeneracy of the entire solution for the $N$-Laplace Liouville equation [PDF]
arXiv, 2022 In this note, we prove the nondegenracy of the explicit finite-mass solution to the $N$-Laplace Liouville equation on the whole space, which is recently shown to be unique up to scaling and translation.
arxiv
Generalization of the Keller-Osserman theorem for higher order differential inequalities [PDF]
, 2018 We obtain exact conditions guaranteeing that any global weak solution of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}^n $$ is trivial, where $m, n \ge 1$ are integers and $a_\alpha$ and $g$ are some functions.
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On a Dini type blow-up condition for nonlinear higher order differential inequalities [PDF]
arXiv, 2023 We obtain a Dini type blow-up condition for global weak solutions of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}^n, $$ where $m, n \ge 1$ are integers and $a_\alpha$ and $g$ are some functions.
arxiv
An upper bound for the least energy of a sign-changing solution to a zero mass problem
Advanced Nonlinear StudiesWe give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation −Δu=f(u),u∈D1,2(RN), $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\right),$ where N ≥ 5 and the nonlinearity f is
Clapp Mónica +2 more
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