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This paper concerns a class of infinite horizon optimal control problems withstate constraints. By extending the needle variation method to the infinitehorizon case we obtain a complete set of necessary optimality conditions for astrong local minimizer in form of the Pontryagin maximum principle and thevalidity of several transversality conditions at infinity. To this purpose, wedevelop an approach in the space of continuous functions converging atinfinity. The considerations including new results on optimality andtransversality conditions, on Banach spaces of continuous functions, on theneedle variation method and on problems with state constraints on the unboundedtime horizon.

Pontryagin's Maximum Principle for Infinite Horizon Optimal Control Problems with Bounded Processes and with State Constraints