scholarly journals Entire solutions of certain partial differential equations and factorization of partial derivatives

2004 ◽  
Vol 357 (8) ◽  
pp. 3169-3177 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Entire Solutions ◽  
Partial Differential ◽  
Partial Derivatives

scholarly journals Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

2019 ◽  
Vol 52 (1) ◽  
pp. 482-489 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv ◽  
Liana Smolovyk
Keyword(s):  
Partial Differential Equations ◽  
Continuous Function ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Positive Continuous Function ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Fixed Direction

AbstractIn the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂn) the following inequality holds{{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}},where L : ℂn → ℝ+ is a positive continuous function, {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

scholarly journals Entire Solutions of

2005 ◽  
Vol 178 ◽  
pp. 151-162 ◽  
Author(s):  
Bao Qin li
Keyword(s):  
Entire Function ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Entire Solutions ◽  
Partial Differential

The paper is concerned with description of entire solutions of the partial differential equations where m ≥ 2, n ≥ 2 are integers and g is a polynomial or an entire function in C2. Descriptions are given and complemented by various examples.

An Equivalent Form of Picard’s Theorem and Beyond

2018 ◽  
Vol 61 (1) ◽  
pp. 142-148 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Functional Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Equivalent Form ◽  
Entire Solutions ◽  
Partial Differential ◽  
Picard’S Theorem ◽  
Picard's Theorem

AbstractThis paper gives an equivalent form of Picard’s theorem via entire solutions of the functional equation f2 + g2 = 1 and then its improvements and applications to certain nonlinear (ordinary and partial) differential equations.

Inequalities for Partial Derivatives and their Applications

2015 ◽  
Vol 58 (3) ◽  
pp. 486-496 ◽  
Author(s):  
Dinh Thanh Duc ◽  
Nguyen Du Vi Nhan ◽  
Nguyen Tong Xuan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Inequalities ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Weighted Integral

AbstractWe present various weighted integral inequalities for partial derivatives acting on products and compositions of functions that are applied in order to establish some new Opial-type inequalities involving functions of several independent variables. We also demonstrate the usefulness of our results in the field of partial differential equations.

ON ENTIRE SOLUTIONS OF FERMAT TYPE PARTIAL DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 15 (05) ◽  
pp. 473-485 ◽  
Author(s):  
BAO QIN LI
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Entire Solutions ◽  
Partial Differential

We shall consider Fermat type partial differential equations in Cn, and give description and classification for entire solutions of the equations.

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