Abstract
This paper is concerned with the existence and multiplicity of normalized solutions to the following biharmonic Schrödinger equation:
where \(\varepsilon , c>0,\) \(N\ge 1,\) \(2<p<2+\frac{8}{N},\) \(\lambda \in {\mathbb {R}}\) is a Lagrangian multiplier and \(h:{\mathbb {R}}^N\rightarrow {{\mathbb {R}}}\) is a continuous function. Under a class of reasonable assumptions on h, we obtain the existence of ground-state normalized solutions. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximus points of h when \(\varepsilon \) is small enough. Some recent results are generalized and improved.
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Zhang, Z., Liu, J. & Guan, Q. Existence and Multiplicity of Normalized Solutions to Biharmonic Schrödinger Equations with Subcritical Growth. Bull. Iran. Math. Soc. 49, 80 (2023). https://doi.org/10.1007/s41980-023-00823-2
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DOI: https://doi.org/10.1007/s41980-023-00823-2