Some topics in symmetrization

BaernsteinII, Albert

doi:10.1007/bfb0086796

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…Thus, by combining Equations ( 12) and ( 22)-( 24), we deduce that , which is a contradiction with Equation (20). Therefore, in this case, we conclude that (u 0 , v 0 ) = (0, 0).…”

Section: Ground State Solutionsmentioning

confidence: 73%

Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases

Ouyang

2023

Mathematics

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We investigate a class of fractional linearly coupled Choquard systems. For the subcritical case and all critical cases, we prove the existence, nonexistence and symmetry of positive ground state solutions of systems, by using the Nehari manifold method, the Pohožaev identity and the Schwartz symmetrization rearrangements. In particular, we overcome the lack of compactness of the critical nonlinearities by using the behaviour of sufficiently small Nehari energy levels.

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“…Thus, by combining Equations ( 12) and ( 22)-( 24), we deduce that , which is a contradiction with Equation (20). Therefore, in this case, we conclude that (u 0 , v 0 ) = (0, 0).…”

Section: Ground State Solutionsmentioning

confidence: 73%

Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases

Ouyang

2023

Mathematics

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“…Moreover, (see [5, Theorem 3]) and which implies where is the Schwartz symmetrization of . Then, every minimizing sequence can be assumed radially symmetric, nonnegative and decreasing in .…”

Section: Minimizing Sequences and Lagrange Multipliersmentioning

confidence: 99%

Existence of solution for a class of activator–inhibitor systems

Figueiredo¹,

Montenegro²

2022

Glasgow Math. J.

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We prove the existence of a solution for a class of activator–inhibitor system of type $- \Delta u +u = f(u) -v$ , $-\Delta v+ v=u$ in $\mathbb{R}^{N}$ . The function f is a general nonlinearity which can grow polynomially in dimension $N\geq 3$ or exponentiallly if $N=2$ . We are able to treat f when it has critical growth corresponding to the Sobolev space we work with. We transform the system into an equation with a nonlocal term. We find a critical point of the corresponding energy functional defined in the space of functions with norm endowed by a scalar product that takes into account such nonlocal term. For that matter, and due to the lack of compactness, we deal with weak convergent minimizing sequences and sequences of Lagrange multipliers of an action minima problem.

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