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JIMO

Motivated by instability analysis of unstable (excited state) solutions
in computational physics/chemistry, in this paper, the minimax method
for solving an optimal control problem with partially uncontrollable variables
is embedded into a more general min-equilibrium problem. Results in saddle
critical point analysis and computation are modified to
provide more information on the minimized objective values and their
corresponding riskiness for one to choose in decision making. A numerical
algorithm to compute such minimized objective values and their corresponding
riskiness is devised. Some convergence results of the algorithm are also
established.

PROC

The aim of this paper is to numerically investigate multiple solutions of
semilinear elliptic systems with zero Dirichlet boundary conditions

-$\Delta u=F_u(x;u,v),$ $x\in\Omega,

-$\Delta v=F_v(x;u,v),$ $x\in\Omega,

where $\Omega \subset \mathbb{R}^{N}$ ($N\ge 1$) is a bounded domain. A strongly coupled case where the potential $F(x;u,v)$ takes the form $|u|^{\alpha_1}|v|^{\alpha_2}$ with $\alpha_1, \alpha_2>1$ is specially studied. By using a local min-orthogonal method, both positive and sign-changing solutions are found and displayed.

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