Classification of solutions for an integral equation
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Publication:5469023
DOI10.1002/cpa.20116zbMath1093.45001OpenAlexW2107784368MaRDI QIDQ5469023
Biao Ou, Wenxiong Chen, Congming Li
Publication date: 16 May 2006
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.20116
monotone solutionradially symmetric solutionsemilinear partial differential equationsIntegral equationmoving planes methodpositive regular solution
Nonlinear boundary value problems for linear elliptic equations (35J65) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Positive solutions of integral equations (45M20)
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Choquard type, Liouville theorems for nonnegative solutions to Hardy-Hénon type system on a half space, Multiple high energy solutions for fractional Schrödinger equation with critical growth, Symmetry of positive solutions for systems of fractional Hartree equations, Reverse conformally invariant Sobolev inequalities on the sphere, Quantitative analysis of a system of integral equations with weight on the upper half space, Nonexistence of positive solutions to \(n\)-th order equations in \(\mathbb{R}^n\), Radial symmetry and monotonicity of the positive solutions for \(k\)-Hessian equations, Monotonicity and symmetry of solutions to fractional \(p\)-Laplacian systems, Qualitative properties and classification of solutions to elliptic equations with Stein-Weiss type convolution part, Sliding methods for a class of generalized fractional Laplacian equations, Qualitative properties of singular solutions of Choquard equations, Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on \(\mathbb{S}^n\), Uniqueness for the nonlocal Liouville equation in \(\mathbb{R}\), Hopf's lemmas for parabolic fractional \(p\)-Laplacians, A priori bounds and existence of positive solutions for fractional Kirchhoff equations, Multiple positive bound state solutions for fractional Schrödinger-Poisson system with critical growth, Maximum principles and Liouville results for uniformly elliptic nonlocal Bellman system, Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities, Liouville type theorem for weighted integral system with negative exponents, Classification of nonnegative solutions to Schrödinger equation with logarithmic nonlinearity, Monotonicity results for quasilinear fractional systems in epigraphs, The sliding method for fractional Laplacian systems, Symmetry and monotonicity of positive solutions for a system involving fractional p\&q-Laplacian in \(\mathbb{R}^n\), On the singularly perturbation fractional Kirchhoff equations: critical case, Infinitely many sign-changing solutions of a critical fractional equation, Higher order Brezis-Nirenberg problem on hyperbolic spaces: existence, nonexistence and symmetry of solutions, Complete metrics with constant fractional higher order \(Q\)-curvature on the punctured sphere, Supersolutions to nonautonomous Choquard equations in general domains, Nondegeneracy of solutions to the critical p$p$‐Laplace Kirchhoff equation, Overdetermined problems for negative power integral equations on bounded domain, Classical solutions to a Hartree type system, Classification of solutions for mixed order conformally system with Hartree-type nonlinearity in ℝn, The global solution and blowup of a spatiotemporal EIT problem with a dynamical boundary condition, Nonlinear inequalities with double Riesz potentials, Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity, A direct method of moving planes for the fractional \(p\)-Laplacian system with negative powers, Qualitative properties for solutions to conformally invariant fourth order critical systems, Liouville type theorems for poly-harmonic Dirichlet problems of Hénon-Hardy type equations on a half space or a ball, Monotonicity of solutions for weighted fractional parabolic equations on the upper half space, Qualitative properties for some integral systems involving Riesz potentials, Asymptotic monotonicity of positive solutions for fractional parabolic equation on the right half space, On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order, A nonexistence result for the Choquard-type Hamiltonian system, Classification and qualitative analysis of positive solutions of the nonlinear Hartree type system, Maximum principles and qualitative properties of solutions for nonlocal double phase operator, Critical conditions and asymptotics for discrete systems of the Hardy-Littlewood-Sobolev type, Nonexistence of solutions for tempered fractional parabolic equations, The radial symmetry of positive solutions for semilinear problems involving weighted fractional Laplacians, Classification of solutions to several semi-linear polyharmonic equations and fractional equations, The aggregation-diffusion equation with energy critical exponent, Asymptotic decay of solutions for sublinear fractional Choquard equations, Multiple positive bound state solutions for fractional Schrödinger-Poisson system with critical nonlocal term, On the fractional Kirchhoff equation with critical Sobolev exponent, Asymptotic behavior of ground states and local uniqueness for fractional Schrödinger equations with nearly critical growth, A heat equation approach to intertwining, Properties of Solutions to Fractional Laplace Equation with Singular Term, Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion, Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities, Liouville theorem and qualitative properties of solutions for an integral system, Uniqueness and some related estimates for Dirichlet problem with fractional Laplacian, Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods, On Liouville theorems of a Hartree–Poisson system, Liouville type theorems for fractional parabolic problems, Maximum principles involving the uniformly elliptic nonlocal operator, Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth, Stein-Weiss type inequality on the upper half space and its applications, An approach to elliptic equations with nonlinear gradient terms via a modulation framework, Asymptotic symmetry and monotonicity of solutions for weighted fractional parabolic equations, Existence and blow-up behavior of positive solutions to integral equations on bounded domains, An anisotropic tempered fractional \(p\)-Laplacian model involving logarithmic nonlinearity, A priori estimates and Liouville type theorems for semilinear equations and systems with fractional Laplacian, Unnamed Item
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