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Existence of Infinitely Many Solutions for Singular Semilinear Problems on Exterior Domains
Article proving the existence of infinitely many radial solutions of โ๐+๐พ(๐) ฦ (๐) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in โแดบ with u = 0 on โBR and lim/rโโ ๐(๐) = 0 where N > 2, f is odd with f < 0 on (0, ฮฒ), f > 0 on (ฮฒ, โ), f is superlinear for large u, ฦ(๐) โผ โ1/(|๐|๐ฒโปยน๐) with 0 < q < 1 for small u, and 0 < ๐พ(๐) โค ๐พโ/rโ with ๐ + q(๐ โ 2) < โ < 2(๐โ 1) for large r.
Date:
March 9, 2018
Creator:
Iaia, Joseph A.
System:
The UNT Digital Library
Loitering at the hilltop on exterior domains
In this article, the author proves the existence of an infinite number of radial solutions of ฮu+f(u)=0 on the exterior of the ball of radius R>0 centered at the origin and f is odd with f<0 on (0,ฮฒ), f>0 on (ฮฒ,ฮด), and fโก0 for u>ฮด. The primitive F(u)=โซu0f(t)dt has a "hilltop" at u=ฮด which allows one to use the shooting method and ODE techniques to prove the existence of solutions.
Date:
November 23, 2015
Creator:
Iaia, Joseph A.
System:
The UNT Digital Library