Kód: 08242714
We consider the semilinear elliptic equation u = p(x)f(u) on a domain Rn, n 3, where f is a nonnegative function which vanishes at the origin and satis es g1 f g2 where g1; g2 are nonnegative, nondecreasing functions which also va ... celý popis
Nákupem získáte 150 bodů
We consider the semilinear elliptic equation u = p(x)f(u) on a domain Rn, n 3, where f is a nonnegative function which vanishes at the origin and satis es g1 f g2 where g1; g2 are nonnegative, nondecreasing functions which also vanish at the origin, and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary. For bounded, we show that a nonnegative solution u satisfying u(x) ! 1 as x ! @ exists provided the function (s) Rs 0 f(t) dt satis es R1 1 [ (s)] 1=2 ds lt; 1. For unbounded (including = Rn), we show that a similar result holds where u(x) ! 1 as jxj ! 1 within and u(x) ! 1 as x ! @ if p(x) decays to zero rapidly as jxj ! 1.
Zařazení knihy Knihy v angličtině Society & social sciences Education
1502 Kč
Osobní odběr Praha, Brno a 12903 dalších
Copyright ©2008-24 nejlevnejsi-knihy.cz Všechna práva vyhrazenaSoukromíCookies
Nákupní košík ( prázdný )