Fractional \(p\)-sub-Laplacian operator problem with concave-convex nonlinearities on homogeneous groups

DOI10.3934/era.2021036zbMath1489.43009OpenAlexW3164560274MaRDI QIDQ2055163

Dengyun Yang, Jinguo Zhang

Publication date: 3 December 2021

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/era.2021036

zbMATH Keywords

Nehari manifoldconcave-convex nonlinearitieshomogeneous groupsfractional \(p\)-sub-Laplacian

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

• Quantization on nilpotent Lie groups
• On some critical problems for the fractional Laplacian operator
• Mountain pass solutions for non-local elliptic operators
• Nehari manifold for non-local elliptic operator with concave-convex nonlinearities and sign-changing weight functions
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Fractional Laplacians, perimeters and heat semigroups in Carnot groups
• Variational methods for non-local operators of elliptic type
• Lyapunov-type inequalities for the fractional \(p\)-sub-Laplacian
• Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
• Multiplicity of positive solutions for a nonlocal elliptic problem involving critical Sobolev-Hardy exponents and concave-convex nonlinearities
• Nonlocal elliptic systems involving critical Sobolev-Hardy exponents and concave-convex nonlinearities
• Three solutions for a fractional elliptic problem with critical and supercritical growth
• Multiplicity of positive solutions for fractional Laplacian equations involving critical nonlinearity
• Fractional eigenvalues
• Asymptotic behaviours in fractional Orlicz-Sobolev spaces on Carnot groups
• A concave—convex elliptic problem involving the fractional Laplacian
• APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Mass and asymptotics associated to fractional Hardy–Schrödinger operators in critical regimes
• MULTIPLE SOLUTIONS FOR A FRACTIONAL LAPLACIAN SYSTEM INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS AND HOMOGENEOUS TERM
• Existence results for a fractional elliptic system with critical Sobolev‐Hardy exponents and concave‐convex nonlinearities
• Fractional p-eigenvalues
• Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities
• A Pólya–Szegö principle for general fractional Orlicz–Sobolev spaces