Some results on semilinear systems on the unbounded space R3.

J. M. Mercier

Revista Matemática Complutense (2000)

  • Volume: 13, Issue: 1, page 207-229
  • ISSN: 1139-1138

Abstract

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We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the E1 E2 = + 1 cases that we exhibit using eigenvalue comparison and ordinary differential equation type arguments.

How to cite

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Mercier, J. M.. "Some results on semilinear systems on the unbounded space R3.." Revista Matemática Complutense 13.1 (2000): 207-229. <http://eudml.org/doc/44394>.

@article{Mercier2000,
abstract = {We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the E1 E2 = + 1 cases that we exhibit using eigenvalue comparison and ordinary differential equation type arguments.},
author = {Mercier, J. M.},
journal = {Revista Matemática Complutense},
keywords = {Ecuaciones diferenciales elípticas; Ondas progresivas; Sistemas diferenciales; Ecuaciones diferenciales en derivadas parciales; unbounded space; semilinear elliptic systems; symmetric solutions},
language = {eng},
number = {1},
pages = {207-229},
title = {Some results on semilinear systems on the unbounded space R3.},
url = {http://eudml.org/doc/44394},
volume = {13},
year = {2000},
}

TY - JOUR
AU - Mercier, J. M.
TI - Some results on semilinear systems on the unbounded space R3.
JO - Revista Matemática Complutense
PY - 2000
VL - 13
IS - 1
SP - 207
EP - 229
AB - We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the E1 E2 = + 1 cases that we exhibit using eigenvalue comparison and ordinary differential equation type arguments.
LA - eng
KW - Ecuaciones diferenciales elípticas; Ondas progresivas; Sistemas diferenciales; Ecuaciones diferenciales en derivadas parciales; unbounded space; semilinear elliptic systems; symmetric solutions
UR - http://eudml.org/doc/44394
ER -

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