The authors prove existence and multiplicity of nontrivial weak solutions to the logarithmic Schrödinger equation using a new perturbative variational approach that overcomes the lack of C1-smoothness in the associated functional.
Willem.Minimax theorems, volume 24 ofProgress in Nonlinear Differential Equations and their Applications
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Existence of solutions is established via variational methods for nonlinear elliptic problems combining HLS and SH critical exponents with subcritical and critical growth.
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On a class of logarithmic Schr\"odinger equations via perturbation method
The authors prove existence and multiplicity of nontrivial weak solutions to the logarithmic Schrödinger equation using a new perturbative variational approach that overcomes the lack of C1-smoothness in the associated functional.
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On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent
Existence of solutions is established via variational methods for nonlinear elliptic problems combining HLS and SH critical exponents with subcritical and critical growth.