Geodesic
Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B15, 34C25, 35K35
Keywords: fourth-order ordinary differential equation, variational method, Brezis-Nirenberg's theorem 
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     author = {Gyulov, Tihomir and Tersian, Stepan},
     title = {Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a155/}
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Gyulov, Tihomir; Tersian, Stepan. Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a155/