A note on the radial solutions for the supercritical Hénon equation

We study the following polyharmonic Hénon equation:where (m)* = 2N/(N – 2m) is the critical exponent, B1(0) is the unit ball in ℝN, N ⩾ 2m + 2 and K(|y|) is a bounded function. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.

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4 Radial solutions

Kinetic Equations ◽

10.1515/9783110550986-005 ◽

2020 ◽

pp. 81-108

Keyword(s):

Radial Solutions

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Asymptotic behaviour of ground state solutions for the fractional Hénon equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125456 ◽

2021 ◽

pp. 125456

Author(s):

Haixia Chen ◽

Xiaolin Xu ◽

Xiaolong Yang

Keyword(s):

Asymptotic Behaviour ◽

Ground State ◽

Ground State Solutions ◽

Hénon Equation

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The exterior Dirichlet problems of Monge–Ampère equations in dimension two

Boundary Value Problems ◽

10.1186/s13661-020-01476-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Limei Dai

Keyword(s):

Asymptotic Behavior ◽

Unit Ball ◽

Bounded Domain ◽

Viscosity Solutions ◽

Sufficient Conditions ◽

Radial Solutions ◽

Dirichlet Problems ◽

Necessary And Sufficient ◽

Monge Ampere ◽

Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

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On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

Mathematics and Mechanics of Solids ◽

10.1177/1081286521994258 ◽

2021 ◽

pp. 108128652199425

Author(s):

Noelia Bazarra ◽

José R Fernández ◽

Ramón Quintanilla

Keyword(s):

Numerical Simulations ◽

Exponential Decay ◽

Time Variable ◽

Radial Solutions ◽

Radially Symmetric Solutions ◽

Thermoelastic Theory

In this paper, we consider the Moore–Gibson–Thompson thermoelastic theory. We restrict our attention to radially symmetric solutions and we prove the exponential decay with respect to the time variable. We demonstrate this fact with the help of energy arguments. Later, we give some numerical simulations to illustrate this behaviour.

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