Variational methods for elliptic systems

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Existence of Solutions for a Class of Semilinear Elliptic Systems via Variational Methods

2013
This is concerned with the existence of solutions to a class of semilinear elliptic systems of the form $$\displaystyle{\left \{\begin{array}{ll} - div(a(x)\nabla u) = \lambda F_{u}(x,u,v)&\mathrm{in}\,\varOmega, \\ - div(b(x)\nabla v) = \lambda F_{v}(x,u,v) &\mathrm{in}\,\varOmega, \\ u = v = 0 &\mathrm{on}\,\partial \varOmega, \end{array} \right.}
G. A. Afrouzi, M. Mirzapour
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Variational Methods for Boundary Value Problems for Systems of Elliptic Equations.

The American Mathematical Monthly, 1965
A. Friedman, M. A. Lavrent'ev
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Variational approach to noncoercive systems of elliptic variational inequalities via trapping region†

Complex Variables and Elliptic Equations, 2012
Siegfried Carl
exaly

Variational methods for indefinite superlinear homogeneous elliptic problems

Nonlinear Differential Equations and Applications, 1995
Henri Berestycki, Louis Nirenberg
exaly

Variational methods and semi-linear elliptic equations

Archive for Rational Mechanics and Analysis, 1986
J R Ward
exaly

Progress in variational methods in Hamiltonian systems and elliptic equations

1992
GIRARDI, Mario, Matzeu M, Pacella F.
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A priori estimates for a semilinear elliptic system without variational structure and their applications

Mathematische Annalen, 2002
Henghui Zou
exaly