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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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Abstract: Our concern is to solve the nonlinear perturbation problem for the semilinear elliptic equation $\Delta u + p(x) u + \phi(x,u) = 0$ in an exterior domain of $\mathbb{R}^N$ with $N \ge 3$. The lower limit of the nonlinear perturbed term $\phi(x,u)$ 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: http://dx.doi.org/10.1090/S0002-9939-04-07489-1
PII: S 0002-9939(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