Influence of nonlinear perturbed terms on the oscillation of elliptic equations

Authors:
Naoto Yamaoka and Jitsuro Sugie

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2281-2290

MSC (2000):
Primary 35B05, 35B20; Secondary 34C10, 35J60

Published electronically:
March 25, 2004

MathSciNet review:
2052404

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Our concern is to solve the nonlinear perturbation problem for the semilinear elliptic equation in an exterior domain of with . The lower limit of the nonlinear perturbed term is given for all nontrivial solutions to be oscillatory. The tools for obtaining our theorems are the so-called ``supersolution-subsolution'' method and some results concerning the oscillation and nonoscillation of solutions of the ordinary differential equation associated with the elliptic equation. A simple example is given to illustrate the main results.

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Additional Information

**Naoto Yamaoka**

Affiliation:
Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan

Email:
yamaoka@math.shimane-u.ac.jp

**Jitsuro Sugie**

Affiliation:
Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan

Email:
jsugie@math.shimane-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-04-07489-1

Keywords:
Oscillation,
nonlinear perturbation,
elliptic equation,
exterior domain,
supersolution-subsolution method

Received by editor(s):
March 17, 2003

Published electronically:
March 25, 2004

Additional Notes:
The second author was supported in part by Grant-in-Aid for Scientific Research 11304008

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2004
American Mathematical Society