Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space
From MaRDI portal
Publication:2017813
DOI10.1007/s00526-014-0727-8zbMath1316.35291arXiv1511.02346OpenAlexW1980911229MaRDI QIDQ2017813
Publication date: 23 March 2015
Published in: Calculus of Variations and Partial Differential Equations, Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1511.02346
Pseudodifferential operators as generalizations of partial differential operators (35S05) Integro-partial differential equations (45K05) Critical exponents in context of PDEs (35B33) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Entire solutions to PDEs (35B08) Symmetries, invariants, etc. in context of PDEs (35B06) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)
Related Items
Qualitative properties of positive solutions for mixed integro-differential equations, Symmetry of components and Liouville-type theorems for semilinear elliptic systems involving the fractional Laplacian, Symmetry and monotonicity of solutions for equations involving the fractional Laplacian of higher order, Nonlinear fractional elliptic systems with boundary measure data: existence and a priori estimates, Radial symmetry results for fractional Laplacian systems, A priori bounds and the existence of positive solutions for weighted fractional systems, Liouville-type theorem for a nonlocal operator on the half plane, Direct method of moving planes for logarithmic Laplacian system in bounded domains, Semilinear integro-differential equations. II: One-dimensional and saddle-shaped solutions to the Allen-Cahn equation, Liouville type theorem for fractional Laplacian system, On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results, Monotonicity of solutions for a class of uniformly elliptic nonlocal Bellman systems, Property of solutions for elliptic equation involving the higher-order fractional Laplacian in \(\mathbb{R}^n_+\), A nonlinear elliptic problem involving the gradient on a half space, Monotonicity of positive solutions for fractional \(p\)-systems in unbounded Lipschitz domains, Liouville-type theorems for a system governed by degenerate elliptic operators of fractional orders, On positive supersolutions of fractional elliptic equations with gradient terms, Classification of anti-symmetric solutions to the fractional Lane-Emden system, Symmetry and non-existence of positive solutions for fractional \(p\)-Laplacian systems, Asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space, A nonexistence result for the Choquard-type Hamiltonian system, Liouville theorem for the fractional Lane-Emden equation in an unbounded domain, Asymptotic decay of solutions for sublinear fractional Choquard equations, Maximum principles for Laplacian and fractional Laplacian with critical integrability, Liouville type theorems for fractional parabolic problems, Maximum principles involving the uniformly elliptic nonlocal operator, A Liouville's theorem for a fractional elliptic system with indefinite nonlinearities, A priori estimates and Liouville type theorems for semilinear equations and systems with fractional Laplacian, Symmetry of solutions for a fractional system, Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian, Monotonicity of solutions for the system with pseudo-relativistic Schrödinger operators, A note on positive supersolutions of the fractional Lane-Emden system, A note on the monotonicity of solutions for fractional equations in half-spaces, Non-existence of positive solutions for a higher order fractional equation, A priori bounds and existence result of positive solutions for fractional Laplacian systems, Liouville's theorem for a fractional elliptic system, Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains, Maximum Principles and Aleksandrov--Bakelman--Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions, Symmetry of positive solutions to quasilinear fractional systems, Monotonicity of positive solutions for nonlocal problems in unbounded domains, Nonexistence of solutions for indefinite fractional parabolic equations, Maximum principles and ABP estimates to nonlocal Lane-Emden systems and some consequences, Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system, On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures, Unnamed Item, Liouville type theorems for PDE and IE systems involving fractional Laplacian on a half space, Monotonicity of solutions for some nonlocal elliptic problems in half-spaces, Symmetry results in the half-space for a semi-linear fractional Laplace equation, Liouville type results for systems of equations involving fractional Laplacian in exterior domains, Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space, A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\), Liouville type theorems for fractional and higher-order fractional systems, Liouville-type theorems for sign-changing solutions to nonlocal elliptic inequalities and systems with variable-exponent nonlinearities, Liouville theorem for fractional Hénon–Lane–Emden systems on a half space, Regularity and nonexistence of solutions for a system involving the fractional Laplacian, Existence and multiplicity of solutions for a class of fractional elliptic systems, Classification of anti-symmetric solutions to nonlinear fractional Laplace equations, Minimal energy solutions to the fractional Lane-Emden system: existence and singularity formation, Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space, Regularity and existence of positive solutions for a fractional system, On positive viscosity solutions of fractional Lane-Emden systems, Monotonicity results for quasilinear fractional systems in epigraphs, Symmetry results for positive solutions of mixed integro-differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fundamental solutions and Liouville type theorems for nonlinear integral operators
- A Harnack inequality for fractional Laplace equations with lower order terms
- Large solutions to elliptic equations involving fractional Laplacian
- Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
- Topics in regularity and qualitative properties of solutions of nonlinear elliptic equations
- Nonexistence results for a class of fractional elliptic boundary value problems
- Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space
- Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations
- A Liouville type theorem for an integral system
- On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
- Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
- Regularity of the obstacle problem for a fractional power of the laplace operator
- Regularity theory for fully nonlinear integro-differential equations
- Existence and non-existence results for fully nonlinear elliptic systems
- A priori bounds for positive solutions of nonlinear elliptic equations
- On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations
- RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN
- Existence Results for Nonproper Elliptic Equations Involving the Pucci Operator
