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Uniqueness of radial solutions for -Laplacian equations in low dimensions
Patrizia Pucci, Jianjun Zhang, Xuexiu Zhong
This paper extends the uniqueness results of Serrin and Tang [\textit{Indiana Univ. Math. J.}, 49 (2000), pp. 897--923] to the low-dimensional case with . We c…
Multiple normalized solutions for two coupled Gross-Pitaevskii equations with attractive interactions and mass constriants
Zhang Jianjun, Zhong Xuexiu, Zhou Jinfang
We are concerned with the following system of two coupled time-independent Gross-Pitaevskii equations $$ \begin{cases} -Δu+λ_1 u=μ_1|u|^{p-2}u+να|u|^{α-2}|v|^βu ~\hbox{in}~ \R^N,\\…
Normalized solutions of coupled Sobolev critical Schrodinger equations with mass subcritical couplings
Zhang Jianjun, Zhong Xuexiu, Zhou Jinfang
We are concerned with qualitative properties of positive solutions to the following coupled Sobolev critical Schrödinger equations $$ \begin{cases} -Δu+λ_1 u=μ_1|u|^{2^*-2}u+να|u|^…
Serrin-type Overdetermination in Scaling Limits: Sharp Existence and Asymptotic Behavior of Quasi-linear Schrödinger Energy Ground States
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
This paper establishes optimal existence results and limiting profiles for energy ground states of the quasi-linear Schrödinger equation $$ -Δu - Δ(|u|^{2})u + λu = |u|^{p-2}u \qua…