scholarly journals Existence of infinitely many solutions for semilinear problems on exterior domains

2020 ◽  
Vol 19 (9) ◽  
pp. 4269-4284
Author(s):  
Joseph Iaia ◽  
Keyword(s):  
Infinitely Many Solutions ◽  
Exterior Domains ◽  
Semilinear Problems

Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains

2021 ◽  
pp. 1-26
Author(s):  
Weiwei Ao ◽  
Chao Liu ◽  
Liping Wang
Keyword(s):  
Unit Ball ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Infinitely Many Solutions ◽  
Fast Decay ◽  
Exterior Domains ◽  
Slow Decay ◽  
Image Position ◽  
Partial Differ

We consider the fractional elliptic problem: where B1 is the unit ball in ℝ N , N ⩾ 3, s ∈ (0, 1) and p > (N + 2s)/(N − 2s). We prove that this problem has infinitely many solutions with slow decay O(|x|−2s/(p−1)) at infinity. In addition, for each s ∈ (0, 1) there exists P s  > (N + 2s)/(N − 2s), for any (N + 2s)/(N − 2s) < p < P s , the above problem has a solution with fast decay O(|x|2s−N). This result is the extension of the work by Dávila, del Pino, Musso and Wei (2008, Calc. Var. Partial Differ. Equ. 32, no. 4, 453–480) to the fractional case.

scholarly journals Global existence of null-form wave equations in exterior domains

2007 ◽  
Vol 256 (3) ◽  
pp. 521-549 ◽  
Author(s):  
Jason Metcalfe ◽  
Christopher D. Sogge
Keyword(s):  
Global Existence ◽  
Wave Equations ◽  
Exterior Domains

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

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