SIAM Journal on Mathematical Analysis · 1981 · 43 citations · 9 references
Natural SciencesComputer ScienceAlgorithmsComputational MechanicsFinite Element AnalysisBoundary ConditionsBoundary-value ProblemsInitial Value ProblemsUniqueness TheoryElliptic Boundary-value ProblemsInitial-boundary Value ProblemsNonlinear Boundary-value ProblemsUniqueness For Functional Differential EquationsUniqueness In Elliptic EquationsUniqueness Of SolutionsUniqueness TheoremsUniqueness Theorems For Partial Differential Equations
Our main concern is to prove uniqueness-existence theorems for the focal boundary value problem $y^{(n)} = f(x,y, \cdots ,y^{(n - 1)} )$, $y^{(i)} (a) = A_i ,y^{(i)} (b) = A_j ,0 \leqq i \leqq k - 1,k \leqq j \leqq n - 1$. The method of proof for existence is the shooting method. Similar results, but for the $(p,q)$-boundary value problem $y^{(n)} = f(x,y, \cdots ,y^{(n - 1)} )$, $y^{(i)} (a) = A_i ,y^{(i)} (b) = A_j ,0 \leqq i \leqq p - 1,0 \leqq j \leqq q - 1,p + q = n$, were considered by the author in [J. Math. Anal. Appl., 55 (1976), pp. 773–784]. The last result in this paper extends the main result in the above-mentioned article.
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