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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.