- Open Access
Erratum to: Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations
© Li and Wang; licensee Springer 2014
- Received: 18 August 2014
- Accepted: 18 August 2014
- Published: 25 September 2014
The original article was published in Boundary Value Problems 2012 2012:109
In this paper, we give a complementary proof on the paper ‘Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations’.
- complementary proof
- prescribed mean curvature Rayleigh equations
where is T-periodic, and are T-periodic in the first argument, T is a constant.
The paper mentioned above obtained the main result by using Mawhin’s continuation theorem in the coincidence degree theory. Unfortunately, the proof of main result Theorem 3.1 (see ) has a serious problem: where depends on and which is only defined for and cannot be continuously extended; therefore, should not be defined on since can occur, where and .
In this paper, we shall give a complementary proof to correct the errors.
and there exists such that .
In , the authors assume that
(H1): , for all and ;
Under the conditions mentioned above, we prove that (2.4) holds.
which is a contradiction.
Consequently, (2.4) holds.
we can use Mawhin’s continuation theorem on Ω.
The authors would like to thank Professor J Webb for pointing out the errors of the paper .
- Li J, Wang Z: Existence and uniqueness of anti-periodic solutions for prescribed mean curvature Rayleigh equations. Bound. Value Probl. 2012., 2012: 10.1186/1687-2770-2012-109Google Scholar
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