FBVP

AcronymDefinition
FBVPFree Boundary Value Problem
FBVPFriends of Bella Vista Park (Oakland, CA)
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Consequently, problem (14) has at least one positive solution, which implies that the FBVP (3) has at least one positive solution.
Thus Theorem 9 ensures that FBVP (92) has at least one positive solution.
(iv) finding positive solutions of FBVP (20)-(22) is equivalent to finding fixed points of the operator Q on P;
Then FBVP (1)-(2) has at least three positive solutions [x.sub.1], [x.sub.2], and [x.sub.3] satisfying
Therefore, Lemma 4 implies that the FBVP (20)-(22) has at least three positive solutions [y.sub.1], [y.sub.2], and [y.sub.3] satisfying (38); that is, the FBVP (1)-(2) has at least three positive solutions [x.sub.1], [x.sub.2], and [x.sub.3] satisfying (38).
Then, FBVP (49) has at least three positive solutions.
Therefore, the FBVP (49) has at least three positive solutions satisfying
Then FBVP (1.3)(1.4) has at least one solution, provided that
Namely, FBVP (1.3)(1.4) has at least one solution in X.
In this section, we will give a theorem on existence of solutions for FBVP (1.3)(1.5).
Then FBVP (1.3)(1.5) is equivalent to the operator equation
Suppose ([H.sup.1]) and ([H.sup.2]) hold, then FBVP (1.3)(1.5) has at least one solution, provided that