and critical cases. This research highlighted the intricate balance between different types of nonlinearities and their impact on the existence and multiplicity of solutions.

In bounded domain, the situation is very different. Let's define where . Refer to Pokhozhaev's identity,

The boundary term will make it impossible to apply Jeanjean's method. This has led many scholars to explore the problem of normalized solutions on bounded domains in recent years. In addition, there have

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