id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-425	Iaia, Joseph	Existence of solutions for semilinear problems on exterior domains	2020	10	.pdf	application/pdf	4208	238	88	EJDE-2020/34 SEMILINEAR PROBLEMS ON EXTERIOR DOMAINS 5 Then from (2.19) we see that u1(t) ≤ b∗ ( (R∗ − t) + c1e − ∫ t 0 c1d(s) ds ∫ R∗ t (R∗ − s)d(s)e ∫ s 0 c1d(x) dx ds ) . Integrating on (t, R∗) gives D(t)W (t) ≤ b∗ ∫ R∗ t (R∗ − s)d(s)D(s) ds thus from (2.21) and the definition of D(t) we see that∫ R∗ t d(s)u1(s) ds = W (t) ≤ b∗e− ∫ t 0 c1d(s) ds ∫	cache/ejde-425.pdf	txt/ejde-425.txt