Geodesic
Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation
Electronic journal of differential equations, Tome 2004 (2004)
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 
@article{EJDE_2004__2004__a55,
     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},
     year = {2004},
     volume = {2004},
     zbl = {1058.34016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a55/}
}
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%A Tersian,  Stepan
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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__a55/