Existence of ground state solutions for Hamiltonian elliptic systems with gradient terms

Rok, strany: 2015, 141 - 156

In this paper we consider the following Hamiltonian elliptic systems in $\R^N$:

$$ -Δ u+\vec{b}(x)·\nabla_xu+V(x)u = g(x,v), -Δ v-\vec{b}(x)·\nabla_xv+V(x)v = f(x,u). $$

Where $V(x)>0$ is a periodic continuous real function, $\vec{b}(x)=(b₁,…,b_N)\in C¹(\R^N,\R^N)$ satisfies the gauge condition $div\vec{b}(x)=0$, $g(x,v)$, $f(x,u)$ are superlinear at infinity. We establish the existence of ground state solutions without the classical Ambrosetti-Rabinowitz superlinear condition.

ISO 690:

Jin, Y., Yang, M. 2015. Existence of ground state solutions for Hamiltonian elliptic systems with gradient terms. In Mathematica Slovaca, vol. 65, no.1, pp. 141-156. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0012

APA:

Jin, Y., Yang, M. (2015). Existence of ground state solutions for Hamiltonian elliptic systems with gradient terms. Mathematica Slovaca, 65(1), 141-156. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0012