A refined approach for non-negative entire solutions of \(\Delta u + u^p = 0\) with subcritical Sobolev growth

DOI10.1515/ans-2016-6024zbMath1375.35024arXiv1608.07592OpenAlexW3104563816MaRDI QIDQ2409850

John Villavert

Publication date: 16 October 2017

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.07592

zbMATH Keywords

Liouville theoremnon-existencescalar curvature equationLane-Emden equationYamabe equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Entire solutions to PDEs (35B08) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (1)

A Liouville theorem for the subcritical Lane-Emden system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp criteria of Liouville type for some nonlinear systems
• Optimal Liouville-type theorems for noncooperative elliptic Schrödinger systems and applications
• Liouville-type theorems and bounds of solutions of Hardy-Hénon equations
• An integral system and the Lane-Emden conjecture
• On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
• The proof of the Lane-Emden conjecture in four space dimensions
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• A Liouville theorem for the subcritical Lane-Emden system
• Qualitative properties of solutions for an integral equation
• Local asymptotic symmetry of singular solutions to nonlinear elliptic equations
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Uniqueness theorems through the method of moving spheres
• Non-existence of positive solutions of Lane-Emden systems
• Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices
• Non-existence results for semilinear cooperative elliptic systems via moving spheres
• A Liouville theorem for high order degenerate elliptic equations
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• A symmetry problem in potential theory
• The conjectures on conformal transformations of Riemannian manifolds
• Liouville Theorem for a Fourth Order Hénon Equation
• Symmetry of Nonnegative Solutions of Elliptic Equations via a Result of Serrin
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• The Yamabe problem
• A priori bounds for positive solutions of nonlinear elliptic equations
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Estimates of the conformal scalar curvature equation via the method of moving planes
• On positive entire solutions of the elliptic equation Δu + K(x)u^p = 0 and its applications to Riemannian geometry
• Classification of solutions for an integral equation
• A Liouville-type theorem for higher order elliptic systems

This page was built for publication: A refined approach for non-negative entire solutions of \(\Delta u + u^p = 0\) with subcritical Sobolev growth