Positive solutions to nonlinear \(p\)-Laplace equations with Hardy potential in exterior domains

DOI10.1016/j.jde.2006.09.001zbMath1387.35244arXivmath/0604469OpenAlexW1993595171MaRDI QIDQ859523

Vitaly Moroz, Vitali Liskevich, Sofya Lyakhova

Publication date: 16 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604469

zbMATH Keywords

\(p\)-LaplacianPhragmén-Lindelöf principleHardy potentialLiouville theoremsPrüfer transformationimproved Hardy inequality

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items

A note on the Caccioppoli inequality for biharmonic operators, Comparison results for nonlinear equations involving A-harmonic operator, Hardy inequalities for Finsler \(p\)-Laplacian in the exterior domain, Bessel pairs and optimal Hardy and Hardy-Rellich inequalities, Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class, The expected time to end the tug-of-war in a wedge, Uniqueness and asymptotic behavior of positive solution of quasilinear elliptic equations with Hardy potential, Phragmén-Lindelöf theorems for equations with nonstandard growth, Positive solutions for a class of elliptic equations, The second expansion of the unique vanishing at infinity solution to a singular elliptic equation, Caccioppoli-type estimates for a class of nonlinear differential operators, Nonlocal problems with critical Hardy nonlinearity, Principal frequency of \(p\)-sub-Laplacians for general vector fields, Groundstate asymptotics for a class of singularly perturbed \(p\)-Laplacian problems in \({{\mathbb{R}}}^N\), Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms, Picone's identity on hyperbolic space and its applications, Quasilinear elliptic inequalities with Hardy potential and nonlocal terms, Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity, Caccioppoli estimates through an anisotropic Picone’s identity, \(A\)-harmonic Picone's identity with applications, Hardy's inequality for functions vanishing on a part of the boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A nonlinear elliptic PDE with the inverse square potential.
• Positive supersolutions to general nonlinear elliptic equations in exterior domains
• Ground state alternative for \(p\)-Laplacian with potential term
• Local and global behaviour of solutions of quasilinear equations of Emden-Fowler type
• A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
• Asymptotic properties of solutions of differential equations with simple characteristics
• Some remarkable sine and cosine functions
• Sturm-Liouville type problems for the \(p\)-Laplacian under asymptotic non-resonance conditions
• Maximum and comparison principles for operators involving the \(p\)-Laplacian
• Asymptotic behaviour of the first eigenfunction of a Hardy-Sobolev operator.
• On the first eigenfunction of a perturbed Hardy-Sobolev operator
• On a class of singular elliptic problems with first order terms.
• On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities
• Optimizing improved Hardy inequalities
• Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains.
• Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.
• Second-order semilinear elliptic inequalities in exterior domains.
• Nonexistence of local solutions to semilinear partial differential inequalities
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Local behavior of solutions of quasi-linear equations
• Positive solutions to singular semilinear elliptic equations with critical potential on cone-like domains
• On a semilinear elliptic equation with inverse-square potential
• Existence and nonexistence results for quasilinear elliptic equations involving the \(p\)-Laplacian with a critical potential
• An improved Hardy-Sobolev inequality and its application
• Positive super-solutions to semi-linear second-order non-divergence type elliptic equations in exterior domains
• Global and local behavior of positive solutions of nonlinear elliptic equations
• A Picone's identity for the p-Laplacian and applications
• Hardy inequalities with optimal constants and remainder terms
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• ASYMPTOTIC BEHAVIOUR OF MINIMIZING SEQUENCES FOR HARDY'S INEQUALITY
• Sturm--Liouville theory for the p-Laplacian
• Eigenvalues of the Radially Symmetric p ‐Laplacian in R ⁿ
• A CRITICAL PHENOMENON FOR SUBLINEAR ELLIPTIC EQUATIONS IN CONE-LIKE DOMAINS
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Existence and uniqueness of positive solutions for some quasilinear elliptic problems
• Nonexistence results and estimates for some nonlinear elliptic problems
• Variational problems with a \(p\)-homogeneous energy