Infinitely many solutions for the Schrödinger equations in \(\mathbb R^N\) with critical growth
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Publication:657462
DOI10.1016/j.jde.2011.09.032zbMath1235.35104OpenAlexW2030534564MaRDI QIDQ657462
Shusen Yan, Wenyi Chen, Wei, Juncheng
Publication date: 16 January 2012
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2011.09.032
Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for higher-order elliptic equations (35J40) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10)
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Cites Work
- Unnamed Item
- Unnamed Item
- Infinitely many positive solutions for an elliptic problem with critical or supercritical growth
- Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\)
- Stability for strongly coupled critical elliptic systems in a fully inhomogeneous medium
- Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\)
- From one bubble to several bubbles: the low-dimensional case.
- The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
- Infinitely many positive solutions for the nonlinear Schrödinger equations in \(\mathbb R^N\)
- Elliptic equations with critical exponent on spherical caps of \(S^{3}\)
- Non-radial clustered spike solutions for semilinear elliptic problems on \(S^N\)
- On Lin-Ni's conjecture in convex domains
- Global and local behavior of positive solutions of nonlinear elliptic equations
- A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture
- On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems
- Elliptic equations of Yamabe type
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