Saddle solutions for the critical Choquard equation

DOI10.1007/s00526-021-01919-5zbMath1459.35216OpenAlexW3129010205WikidataQ114229017 ScholiaQ114229017MaRDI QIDQ1995238

Xu Zhang, Jiankang Xia

Publication date: 19 February 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-021-01919-5

zbMATH Keywords

Choquard equationsaddle type nodal solutions

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20) Symmetries, invariants, etc. in context of PDEs (35B06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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Multiplicity of solutions to linearly coupled Hartree systems with critical exponent ⋮ Infinitely many non-radial positive solutions for Choquard equations ⋮ Sign-changing solutions to the critical Choquard equation ⋮ Normalized saddle solutions for a mass supercritical Choquard equation ⋮ Normalized solutions to the critical Choquard-type equations with weakly attractive potential and nonlocal perturbation ⋮ Prescribed mass standing waves for energy critical Hartree equations ⋮ Saddle solutions for the Choquard equation with a general nonlinearity ⋮ Signed and sign-changing solutions to the nonlinear Choquard problem with upper critical exponent ⋮ Semi-classical states for the Choquard equations with doubly critical exponents: Existence, multiplicity and concentration ⋮ On critical double phase Choquard problems with singular nonlinearity ⋮ Existence of solutions for nonlinear biharmonic Choquard equations on weighted lattice graphs ⋮ Ground state solutions for Kirchhoff-type problems with convolution nonlinearity and Berestycki-Lions type conditions ⋮ Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities ⋮ Saddle solutions for the fractional Choquard equation ⋮ Existence and asymptotic behavior of ground states for Choquard-Pekar equations with Hardy potential and critical reaction

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