Existence of positive bound states of nonlinear Schrödinger equations with saddle-like potential
From MaRDI portal
Publication:4264286
DOI10.1016/S0362-546X(97)00593-2zbMath0943.35026OpenAlexW1965092832MaRDI QIDQ4264286
Patricio L. Felmer, Manuel A. del Pino, Olímpio Hiroshi Miyagaki
Publication date: 11 May 2000
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00593-2
Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Schrödinger operator, Schrödinger equation (35J10) Variational methods for second-order elliptic equations (35J20)
Related Items
Standing waves for nonlinear Schrödinger equations with a radial potential ⋮ Existence and concentration for Kirchhoff type equations around topologically critical points of the potential ⋮ Spike solutions of a nonlinear Schrödinger equation with degenerate potential ⋮ Existence and concentration of solution for a class of fractional elliptic equation in \(\mathbb {R}^N\) via penalization method ⋮ Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\) ⋮ Multiple homoclinic solutions for a one-dimensional Schrödinger equation ⋮ Semi-classical states for nonlinear Schrödinger equations ⋮ Existence of standing waves solution for a nonlinear Schrödinger equation in \(\mathbb{R}^N\) ⋮ Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems ⋮ Complex dynamics in one-dimensional nonlinear Schrödinger equations with stepwise potential ⋮ Existence of a positive solution for a logarithmic Schrödinger equation with saddle-like potential ⋮ Existence of solutions for an NSE with discontinuous nonlinearity ⋮ Existence of Multi-bump Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations ⋮ Multi-bump standing waves with critical frequency for nonlinear Schrödinger equations ⋮ On singular perturbations of superlinear elliptic systems ⋮ A critical nonlinear fractional elliptic equation with saddle-like potential in ℝN ⋮ Extremal solutions for quasilinear elliptic inclusions in all of \(\mathbb{R}^N\) with state-dependent subdifferentials ⋮ Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations ⋮ Existence and asymptotic behavior of solutions for a class of semilinear subcritical elliptic systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\)
- Positive solutions of some nonlinear elliptic problems in exterior domains
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Variational and topological methods in partially ordered Hilbert spaces
- On a class of nonlinear Schrödinger equations
- Existence of positive solutions of semilinear elliptic equations in \(\mathbb{R}^ N\)
- Semiclassical states of nonlinear Schrödinger equations
- Multi-peak bound states for nonlinear Schrödinger equations
- On a singularly perturbed elliptic equation
- On concentration of positive bound states of nonlinear Schrödinger equations
- On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- On the existence of positive entire solutions of a semilinear elliptic equation
- Local mountain passes for semilinear elliptic problems in unbounded domains
- Positive solutions of the elliptic equation \(\Delta u + u^{(n+2)/(n-2)} + K(x) u^ q =0\) in \(\mathbb{R}^ n\) and in balls
- Correction to existence of semiclassical bound states of nonlinear scierodinger equations with potentials of the, class (V)a
- Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)a
- Homoclinic type solutions for a semilinear elliptic PDE on ℝn
- On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
- On a class of semilinear elliptic problems in ℝN with critical growth
- Extrema problems with critical sobolev exponents on unbounded domains
- Existence of multi-bumb solutions for nonlinear schrödinger equations via variational method
