We consider the following elliptic system: -\Delta u= |v|^{p-1} v + h(x) % & x\in \Omega \\ -\Delta v= |u|^{q-1} u + k(x) % & x\in \Omega \\ u=v=0 & x\in \partial \Omega where \Omega \subset R^N, N\geq 3 is a smooth bounded domain. If h(x)= k(x)= 0 the system presents a natural Z_2 symmetry, which guarantees the existence of infinitely many solutions. In this paper we show that the multiplicity structure can be maintained if (p,q)lies below a suitable curve in R^2.
Perturbation of symmetry and multiplicity of solutions for strongly indefinite elliptic systems / C. Tarsi. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 7:1(2007), pp. 1-30.
Perturbation of symmetry and multiplicity of solutions for strongly indefinite elliptic systems
C. Tarsi
2007
Abstract
We consider the following elliptic system: -\Delta u= |v|^{p-1} v + h(x) % & x\in \Omega \\ -\Delta v= |u|^{q-1} u + k(x) % & x\in \Omega \\ u=v=0 & x\in \partial \Omega where \Omega \subset R^N, N\geq 3 is a smooth bounded domain. If h(x)= k(x)= 0 the system presents a natural Z_2 symmetry, which guarantees the existence of infinitely many solutions. In this paper we show that the multiplicity structure can be maintained if (p,q)lies below a suitable curve in R^2.
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