Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems

DOI10.1006/jdeq.1999.3737zbMath0952.35054OpenAlexW4210799459MaRDI QIDQ1570754

Jaeyoung Byeon

Publication date: 4 January 2001

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

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4040

zbMATH Keywords

positive solutionssemilinear elliptic equationcritical orbital set

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items

Standing waves for nonlinear Schrödinger equations with a radial potential, Multiplicity of positive solutions for a critical quasilinear Neumann problem, Existence and orbital stability of standing waves to nonlinear Schrödinger system with partial confinement, Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations, On the Orbital Stability of Standing-Wave Solutions to a Coupled Non-Linear Klein-Gordon Equation, Existence of the normalized solutions to the nonlocal elliptic system with partial confinement, Existence and stability of a two-parameter family of solitary waves for a 2-coupled nonlinear Schrödinger system, Existence of travelling-wave solutions to a coupled system of Korteweg-de Vries equations, Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems. II, Existence and orbital stability of standing waves for nonlinear Schrödinger systems, Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nodal sets for solutions of elliptic equations
• The principle of symmetric criticality
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• On the number of positive solutions of some weakly nonlinear equations on annular regions
• A nonlinear boundary value problem with many positive solutions
• Rearrangements and convexity of level sets in PDE
• Symmetry and related properties via the maximum principle
• Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli
• Existence of many positive solutions of semilinear equations on annulus
• Multipeak solutions for a semilinear Neumann problem
• Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli
• Minimal submanifolds of low cohomogeneity
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings
• Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0
• A priori bounds for positive solutions of nonlinear elliptic equations
• Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• Existence of large positive solutions of some nonlinear elliptic $si:equations on singularly perturbed doamins
• Existence of multi-bumb solutions for nonlinear schrödinger equations via variational method
• Existence of infinitely many homoclinic orbits in Hamiltonian systems