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- Title
Solvability of a Class of Higher Order Singular Nonlinear Partial Differential Equations.
- Authors
Bacani, Dennis B.; Lope, Jose Ernie C.
- Abstract
This paper studies the singular nonlinear partial differential equation... where Im = {(j, α) ∈ N × Nn ; j + α ≤ m, j < m} and F (t, x, Z) is a function continuous in t and holomorphic in (x, Z). We present a unique solvability result for this class of equations under the assumption that F (t, x, 0) is of order o(1) (as t → 0) uniformly in x and (∂F/∂zj,α)(0, x, 0) ≡ 0 for all (j, α) ∈ lm \{α = 0}. We then extend the unique solvability result to a wider class of equations.
- Subjects
NONLINEAR partial differential operators; UNIQUENESS (Mathematics); EXISTENCE theorems; HOLOMORPHIC functions
- Publication
Southeast Asian Bulletin of Mathematics, 2018, Vol 42, Issue 6, p809
- ISSN
0129-2021
- Publication type
Article