Electron. J. Diff. Eqns., Vol. 2004(2004), No. 41, pp. 1-14.

Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation

Tihomir Gyulov & Stepan Tersian

Abstract:
We study the multiplicity of nontrivial solutions for a semilinear fourth-order ordinary differential equation arising in spatial patterns for bistable systems. In the proof of our results, we use minimization theorems and Brezis-Nirenberg's linking theorem. We obtain also estimates on the minimizers of the corresponding functionals.

Submitted January 5, 2004. Published March 23, 2004.
Math Subject Classifications: 34B15, 34C25, 35K35.
Key Words: Fourth-order ordinary differential equation, variational method, Brezis-Nirenberg's theorem.

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Tihomir Gyulov
C.A.M.I., University of Rousse
8 ``Studentska'' Str., 7017 Rousse, Bulgaria
email: tgyulov@ecs.ru.acad.bg
Stepan Tersian
C.A.M.I., University of Rousse
8 ``Studentska'' Str., 7017 Rousse, Bulgaria
email: tersian@ami.ru.acad.bg

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