Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in \(\mathbb{R}^3\)
From MaRDI portal
Publication:1706347
DOI10.1016/j.jmaa.2018.01.003zbMath1435.35008OpenAlexW2783997552MaRDI QIDQ1706347
Publication date: 22 March 2018
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.01.003
Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Related Items (23)
Existence of infinitely many solutions for a \(p\)-Kirchhoff problem in RN ⋮ Radial stationary solutions to a class of wave system as well as their asymptotical behavior ⋮ On the multiplicity and concentration of positive solutions to a Kirchhoff-type problem with competing potentials ⋮ Positive solutions for a Kirchhoff-type problem involving multiple competitive potentials and critical Sobolev exponent ⋮ Infinitely many nodal solutions for Kirchhoff-type equations with non-odd nonlinearity ⋮ Ground state solutions of Schrödinger-Kirchhoff equations with potentials vanishing at infinity ⋮ Existence and concentration of ground state solutions for Kirchhoff type equations with general nonlinearities ⋮ Existence of positive solutions for Kirchhoff-type problem in exterior domains ⋮ Multiplicity of positive solutions for a Kirchhoff type problem without asymptotic conditions ⋮ Existence of positive solutions to Kirchhoff equations with vanishing potentials and general nonlinearity ⋮ Existence and asymptotic behaviour of ground state solutions for Kirchhoff-type equations with vanishing potentials ⋮ Classification results for Kirchhoff equations in RN ⋮ On the existence of least energy solutions to a Kirchhoff-type equation in \(\mathbb{R}^3\) ⋮ Sign-changing solutions for fractional Kirchhoff-type equations with critical and supercritical nonlinearities ⋮ Unnamed Item ⋮ Choquard-type equation with competing coefficients ⋮ Liouville theorems for Kirchhoff equations in RN ⋮ Existence of positive solution for Kirchhoff type problem with critical discontinuous nonlinearity ⋮ Multiple positive solutions for a class of Kirchhoff type equations with indefinite nonlinearities ⋮ Normalized ground state solutions for Kirchhoff type systems ⋮ A NON-RADIALLY SYMMETRIC SOLUTION TO A CLASS OF ELLIPTIC EQUATION WITH KIRCHHOFF TERM ⋮ Multiple positive solutions to Kirchhoff equations with competing potential functions in \(\mathbb{R}^3\) ⋮ On the Kirchhoff type equations in \(\mathbb{R}^N \)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence and concentration result for the Kirchhoff type equations with general nonlinearities
- Existence of a positive solution to Kirchhoff-type problems without compactness conditions
- Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth
- Variational, topological, and partial order methods with their applications
- The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity.
- Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
- Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
- A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problem
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- Nontrivial solutions of Kirchhoff-type problems via the Yang index
- Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- On a class of nonlinear Schrödinger equations
- Semiclassical states of nonlinear Schrödinger equations
- On concentration of positive bound states of nonlinear Schrödinger equations
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- Local mountain passes for semilinear elliptic problems in unbounded domains
- Minimax theorems
- Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
- Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior
- Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
- The critical problem of Kirchhoff type elliptic equations in dimension four
- Standing waves for nonlinear Schrödinger equations with a general nonlinearity
- Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents
- On the shape of least‐energy solutions to a semilinear Neumann problem
- On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
This page was built for publication: Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in \(\mathbb{R}^3\)
