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- W4292133669 abstract "Using a dual variational approach we obtain nontrivial real-valued solutions of the critical nonlinear Helmholtz equation $$ - Delta u - k^{2}u = Q(x)|u|^{2^{ast} - 2}u, quad u in W^{2,2^{ast}}(mathbb{R}^{N}) $$ for $Ngeq 4$, where $2^{ast} := frac{2N}{N-2}$. The coefficient $Q in L^{infty}(mathbb{R}^{N})setminus{0}$ is assumed to be nonnegative, asymptotically periodic and to satisfy a flatness condition at one of its maximum points. The solutions obtained are so-called dual ground states, i.e., solutions arising from critical points of the dual functional with the property of having minimal energy among all nontrivial critical points. Moreover, we show that no dual ground state exists for $N=3$." @default.
- W4292133669 created "2022-08-17" @default.
- W4292133669 creator A5046755213 @default.
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- W4292133669 date "2017-07-04" @default.
- W4292133669 modified "2023-10-16" @default.
- W4292133669 title "Dual ground state solutions for the critical nonlinear Helmholtz equation" @default.
- W4292133669 doi "https://doi.org/10.48550/arxiv.1707.00959" @default.
- W4292133669 hasPublicationYear "2017" @default.
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