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We study a symmetric nonlinear value problem in all R, arising in nonlinear optics from the study of propagation of electromagnetic guided waves through a layered medium with a nonlinear response. By variational arguments, we prove the existence of a positive asymmetric solution of the problem, corresponding to an asymmetric guided wave.

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An optimal control problem for a nonlinear elliptic equation of logistic type is considered. Under certain assumptions, the existence of at least an optimal control is shown and an optimality system is derived. Then this system is used for proving the uniqueness of and a constructive approximation to the optimal control.

Abstract. An optimal control problem for a nonlinear elliptic equation of logistic type is considered. Under certain assumptions, the existence of at least an optimal control is shown and an optimality system is derived. Then this system is used for proving the uniqueness of and a constructive approximation to the optimal control.