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Existence and Multiplicity of Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains
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This paper focuses on the existence of multiple normalized solutions to Schr\"{o}dinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized ground state by searching for a local minimizer, and the other one is a mountain pass solution. Secondly, using a version of Linking theorems for normalized solutions, we prove the multiplicity of solutions to Schr\"{o}dinger equations in a star-shaped bounded domain. Moreover, we arrive at the existence of nonradial normalized solutions to Schr\"odinger equations in a ball.
Forward citations
Cited by 4 Pith papers
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Existence and multiplicity of normalized solutions to a large class of elliptic equations on bounded domains with general boundary conditions
For sufficiently small prescribed mass, normalized solutions exist, and often many of them exist, for a large class of elliptic boundary value problems with general nonlinearities and several boundary condition types.
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Existence and local uniqueness of multi-spike solutions for Br\'{e}zis-Nirenberg problem with prescribed mass
The authors prove the existence and local uniqueness of multi-peak solutions with prescribed L2 mass for the critical Brézis-Nirenberg problem in dimensions at least six.
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Normalized solutions on large smooth domains to the Schr\"{o}dinger equations with potential and combined nonlinearities: The Sobolev critical case
A variational existence proof for normalized critical NLS solutions on large domains contains a false Liouville step and sign errors, so the main theorems are not established.
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Normalized Solutions on large smooth domains to the Schr\"{o}dinger equation with potential and general nonlinearity: Mass super-critical case
For mass-supercritical nonlinearities with an external potential, positive normalized solutions exist on sufficiently large star-shaped domains and, under a radial condition on the potential, in R^N.
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