We consider a class of semilinear elliptic system of the form -Delta u(x,y)+ abla W(u(x,y))=0,quad (x,y)inR^{2}, where W:R^{2} oR is a double well potential with minima a_pminR^$. We show, via variational methods, that if the set of minimal heteroclinic solutions to the one dimensional system -ddot q(x)+ abla W(q(x))=0, xinR, up to translations, is finite and constituted by not degenerate functions, then the system has infinitely many solutions uin C^{2}(R^{2})^{2}, parametrized by an energy value, which are periodic in the variable y and satisfy lim_{x opminfty}u(x,y)=a_{pm} for any yinR.

Brake orbit solutions for semilinear elliptic systems with asymmetric double well potential / Alessio, FRANCESCA GEMMA; Montecchiari, Piero. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 19:1(2017), pp. 691-717. [10.1007/s11784-016-0370-4]

Brake orbit solutions for semilinear elliptic systems with asymmetric double well potential

ALESSIO, FRANCESCA GEMMA
;
MONTECCHIARI, Piero
2017-01-01

Abstract

We consider a class of semilinear elliptic system of the form -Delta u(x,y)+ abla W(u(x,y))=0,quad (x,y)inR^{2}, where W:R^{2} oR is a double well potential with minima a_pminR^$. We show, via variational methods, that if the set of minimal heteroclinic solutions to the one dimensional system -ddot q(x)+ abla W(q(x))=0, xinR, up to translations, is finite and constituted by not degenerate functions, then the system has infinitely many solutions uin C^{2}(R^{2})^{2}, parametrized by an energy value, which are periodic in the variable y and satisfy lim_{x opminfty}u(x,y)=a_{pm} for any yinR.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/239750
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