A monotone property of the ground state energy to the scalar field equation and applications
From MaRDI portal
Publication:5217910
DOI10.1112/jlms.12234zbMath1458.35200OpenAlexW2944402228WikidataQ127885526 ScholiaQ127885526MaRDI QIDQ5217910
No author found.
Publication date: 26 February 2020
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/jlms.12234
variational methodsground statesingularly perturbed problemvariable exponentclassical nonlinear field equation
Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)
Related Items
Minimization of elliptic non-local functionals involving \(\vec{p}(\cdot)\)-Laplacian ⋮ Concentration phenomena for nonlinear magnetic Schrödinger equations with critical growth ⋮ Extremal functions for a supercritical \(k\)-Hessian inequality of Sobolev-type ⋮ Multi-bump solutions for quasilinear elliptic equations with variable exponents and critical growth in ℝN ⋮ Qualitative analysis on logarithmic Schrödinger equation with general potential ⋮ A class of supercritical Sobolev type inequalities with logarithm and related elliptic equations
Cites Work
- Unnamed Item
- Unnamed Item
- Cordes-Nirenberg theory in variable exponent spaces
- On supercritical Sobolev type inequalities and related elliptic equations
- Localized nodal solutions of higher topological type for semiclassical nonlinear Schrödinger equations
- Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems
- Bound states of nonlinear Schrödinger equations with magnetic fields
- Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters
- Nonlinear scalar field equations. I: Existence of a ground state
- Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- On a class of nonlinear Schrödinger equations
- Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters. II.
- Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
- Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters. III.
- On a superlinear elliptic \(p\)-Laplacian equation.
- Nodal solutions for a supercritical semilinear problem with variable exponent
- Convergence from power-law to logarithm-law in nonlinear scalar field equations
- Weighted variable exponent Sobolev estimates for elliptic equations with non-standard growth and measure data
- On concentration of positive bound states of nonlinear Schrödinger equations
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- On the location and profile of spike-layer nodal solutions to nonlinear Schrödinger equations
- Local mountain passes for semilinear elliptic problems in unbounded domains
- Minimax theorems
- Sign-changing solutions for Schrödinger equations with indefinite supperlinear nonlinearities
- Minimization of quotients with variable exponents
- Existence, multiplicity and profile of sign-changing clustered solutions of a semiclassical nonlinear Schrödinger equation
- Local existence conditions for an equations involving the \(p(x)\)-Laplacian with critical exponent in \(\mathbb R^N\)
- Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials
- \(p(x)\)-Laplacian equations in \(\mathbb R^N\) with periodic data and nonperiodic perturbations
- Monotonicity properties for ground states of the scalar field equation
- Standing waves for nonlinear Schrödinger equations with a general nonlinearity
- Standing waves for nonlinear Schrödinger equations involving critical growth
- On equidistant sets in normed linear spaces
- Spikes of sign-changing solutions to the critical Schrödinger equations with trapping potentials
- Existence and multiplicity results for some superlinear elliptic problems on RN
- Multiplicity results for some nonlinear Schrödinger equations with potentials
- On interacting bumps of semi-classical states of nonlinear Schrödinger equations.
- Solutions concentrating around the saddle points of the potential for critical Schrödinger equations
