Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 201, pp. 118.
Analytic solutions of a class of nonlinear partial differential equations
Eugenia N. Petropoulou
Abstract:
We study a class of nonlinear partial differential equations,
which can be connected with wavetype equations and Laplacetype equations,
by using a functionalanalytic technique.
We establish primarily the existence and uniqueness of bounded
solutions in the twodimensional HardyLebesque space of analytic functions
with independent variables lying in the open unit disc. However these results
can be modified to expand the domain of definition.
The proofs have a constructive character enabling the determination of concrete
and easily verifiable conditions, and the determination of the coefficients
appearing in the power series solution.
Illustrative examples are given related to the sineGordon equation,
the KleinGordon equation, and to equations with nonlinear terms of algebraic,
exponential and logistic type.
Submitted April 29, 2015. Published August 4, 2015.
Math Subject Classifications: 35A01, 35A02, 35B99, 35C10, 35J60, 35L70.
Key Words: Analytic solution; series solution; bounded solution; wavetype PDE;
Laplacetype PDE; PDE with mixed derivatives; sineGordon;
KleinGordon.
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Eugenia N. Petropoulou
Department of Civil Engineering
University of Patras
26500 Patras, Greece
email: jenpetr@upatras.gr

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