Finite Morse index solutions of the fractional Henon-Lane-Emden equation with Hardy potential

DOI10.11650/tjm/211203zbMath1486.35435OpenAlexW4206045655MaRDI QIDQ2119699

Soojung Kim, Youngae Lee

Publication date: 30 March 2022

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11650/tjm/211203

zbMATH Keywords

Hardy potentialmonotonicity formulafinite Morse index solutionfractional Henon-Lane-Emden equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) Critical exponents in context of PDEs (35B33) A priori estimates in context of PDEs (35B45) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local behavior of fractional \(p\)-minimizers
• Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations
• Stable solutions and finite Morse index solutions of nonlinear elliptic equations with Hardy potential
• Nonlocal Harnack inequalities
• Partial regularity of stable solutions to the supercritical equations and its applications
• Hitchhiker's guide to the fractional Sobolev spaces
• Classification of positive solutions of semilinear elliptic equations with Hardy term
• Finite Morse index solutions of an elliptic equation with supercritical exponent
• Some Liouville theorems for Hénon type elliptic equations
• On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
• Sharp constants in the Hardy-Rellich inequalities
• The Wiener test for degenerate elliptic equations
• Spectral theory of the operator \((p^2+m^2)^{1/2}-Ze^2/r\)
• The Dirichlet problem for the \(p\)-fractional Laplace equation
• Remark on some conformally invariant integral equations: the method of moving spheres
• Semilinear elliptic equations for the fractional Laplacian with Hardy potential
• On stable and finite Morse index solutions of the fractional Toda system
• On stable and finite Morse index solutions of the nonlocal Hénon-Gelfand-Liouville equation
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem
• Monotonicity formula and \(\varepsilon\)-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• Quasilinear Dirichlet problems driven by positive sources
• Sharp energy estimates for nonlinear fractional diffusion equations
• Stable solutions of \(-\delta u=e^u\) on \(\mathbb R^N\)
• Uniqueness of Radial Solutions for the Fractional Laplacian
• A concave—convex elliptic problem involving the fractional Laplacian
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• Insufficiency of the étale Brauer-Manin obstruction: Towards a simply connected example
• On stable solutions of the fractional Hénon–Lane–Emden equation
• Some Theorems Concerning 2-Dimensional Brownian Motion
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Nonlocal minimal surfaces
• On the classification of solutions of -Δ𝑢=𝑒^{𝑢} on ℝ^{ℕ}: Stability outside a compact set and applications
• A priori bounds for positive solutions of nonlinear elliptic equations
• The local regularity of solutions of degenerate elliptic equations
• Weighted Norm Inequalities for Fractional Integrals
• Partial regularity of stable solutions to the fractional Geľfand-Liouville equation
• On the fractional Lane-Emden equation
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• An Extension Problem Related to the Fractional Laplacian
• Classification of solutions for an integral equation
• Weighted Norm Inequalities for the Hardy Maximal Function