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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A two end family of solutions for the Inhomogeneous Allen-Cahn equation in R^2
, 2013 In this work we construct a family of entire bounded solution for the singulary perturbed Inhomogeneous Allen-Cahn Equation $\ep^2\div\left(a(x)\nabla u\right)-a(x)F'(u)=0$ in $\R^2$, where $\ep\to 0$.
Agudelo, Oscar, Zuniga, Andres
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Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes [PDF]
, 2012 2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.We study the problem of the global regularity for linear partial differential operators with polynomial coefficients.
Calvo, Daniela +2 more
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Sharp asymptotic expansions of entire large solutions to a class of k-Hessian equations with weights
Advances in Nonlinear AnalysisIt is well-known that it is a quite interesting topic to study the asymptotic expansions of entire large solutions of nonlinear elliptic equations near infinity. But very little is done.
Wan Haitao
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On the H\'enon-Lane-Emden conjecture [PDF]
, 2011 We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$.
In R +3 more
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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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A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
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On blow-up conditions for nonlinear higher order evolution inequalities
, 2023 We obtain exact conditions for global weak solutions of the problem $$ \left\{ \begin{aligned} & u_t - \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, t, u) \ge f (|u|) \quad \mbox{in } {\mathbb R}_+^{n+1} = {\mathbb R}^n ...
Kon'kov, A. A., Shishkov, A. E.
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Existence of positive solutions to semilinear elliptic systems with supercritical growth [PDF]
, 2016 We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth.
Li, Congming, Villavert, John
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Interior estimates of derivatives and a Liouville type theorem for Parabolic $k$-Hessian equations
, 2022 In this paper, we establish the gradient and Pogorelov estimates for $k$-convex-monotone solutions to parabolic $k$-Hessian equations of the form $-u_t\sigma_k(\lambda(D^2u))=\psi(x,t,u)$.
Bao, J. G. +3 more
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