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Normalized solutions for critical Schrödinger equations involving (2,q)-Laplacian

Wei Lulu, Song Yueqiang

Opuscula Mathematica

2025

Vol. 45, no. 5

685--716

In this paper, we consider the following critical Schrödinger equation involving (2, q)-Laplacian: [formula] The meaningful and interesting phenomenon is the simultaneous occurrence of (2, q)-Laplacian and critical nonlinearity in the above equation. In order to obtain existence of multiple normalized solutions for such equation, we need to make a detailed estimate. More precisely, for the L2-subcritical case, we use the truncation technique, concentration-compactness principle and the genus theory to get the existence of multiple normalized solutions. For the L2-supercritical case, we obtain a couple of normalized solution for the above equation by a fiber map and concentration-compactness principle.

On the p-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity

Zhao Min, Song Yueqiang, Repovš Dušan D.

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230124

In this article, we deal with the following p-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: [formula], where [...] and k are some positive parameters, […] is the critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, and functions V and M satisfy the suitable conditions. By proving the compactness results using the fractional version of concentration compactness principle, we establish the existence of nontrivial solutions to this problem.