We seek multiple solutions to systems of semilinear elliptic equations of the type-ΔU(x)=∇H(x; U(x))x∈ΩU(x)=0x∈∂Ω,where Ω⊂RN (N≥1) is a bounded regular domain and U=(u1, u2):Ω→R2. For a class of potentials where the variables are strongly coupled as in the model H(x; u1, u2)=u1α1u2α2 with αi>1, we provide the existence of nine nontrivial solutions characterized by sign properties of each component. © 2000 Academic Press.

Conti, M., Merizzi, L., Terracini, S. (2000). On the existence of many solutions for a class of superlinear elliptic systems. JOURNAL OF DIFFERENTIAL EQUATIONS, 167(2), 357-387 [10.1006/jdeq.2000.3813].

On the existence of many solutions for a class of superlinear elliptic systems

TERRACINI, SUSANNA
2000

Abstract

We seek multiple solutions to systems of semilinear elliptic equations of the type-ΔU(x)=∇H(x; U(x))x∈ΩU(x)=0x∈∂Ω,where Ω⊂RN (N≥1) is a bounded regular domain and U=(u1, u2):Ω→R2. For a class of potentials where the variables are strongly coupled as in the model H(x; u1, u2)=u1α1u2α2 with αi>1, we provide the existence of nine nontrivial solutions characterized by sign properties of each component. © 2000 Academic Press.
Articolo in rivista - Articolo scientifico
Variational setting; critical points; energy functional; multiplicity result; open cones; mini-max arguments; approximating procedure
English
2000
167
2
357
387
none
Conti, M., Merizzi, L., Terracini, S. (2000). On the existence of many solutions for a class of superlinear elliptic systems. JOURNAL OF DIFFERENTIAL EQUATIONS, 167(2), 357-387 [10.1006/jdeq.2000.3813].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18239
Citazioni
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 16
Social impact