Optimal control problem for an elliptic equation which has exactly two solutions

DOI10.1002/OCA.981zbMath1288.49008OpenAlexW2101337323MaRDI QIDQ2847228

Xiaopei Li, Shu Luan, Hang Gao

Publication date: 4 September 2013

Published in: Optimal Control Applications and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/oca.981

zbMATH Keywords

optimal controlsemilinear elliptic equationsPontryagin's maximum principlerelaxed controls

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Existence theories for optimal control problems involving partial differential equations (49J20) Semilinear elliptic equations (35J61)

Related Items (4)

Time optimal control for some ordinary differential equations with multiple solutions ⋮ Nonexistence and existence results of an optimal control problem governed by a class of multisolution semilinear elliptic equations ⋮ A new approach to optimal control of ill-posed semilinear elliptic equations in the absence of convexity ⋮ Quenching time optimal control for some ordinary differential equations

Cites Work

• Necessary conditions for infinite-dimensional control problems
• Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints
• Second-order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations
• Optimal control problems for a class of semilinear multisolution elliptic equations
• Analysis and control of nonlinear infinite dimensional systems
• Optimal control problems with state constraints for semilinear distributed-parameter systems
• Existence of multiple positive solutions of subcritical semilinear elliptic problems in exterior strip domains
• On some elliptic optimal control problems with state constraints
• Optimal Control of Semilinear Multistate Systems with State Constraints
• Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
• Maximum Principle of Optimal Control for Degenerate Quasi-Linear Elliptic Equations
• Optimal control problems governed by non-well-posed semilinear elliptic equation

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