The aims of the submitted project are the following: 1. Formulation and proofs of new principles for existence, uniqueness or multiplicity of solutions of nonlinear regular and singular boundary value problems with quasilinear differential operators. In the singular case nonlinearities in differential equations can have singularities in all variables. 2. Application of obtained principles to singular problems arising in physics and technical practice, for example in the theory of shallow elastic membrane caps. 3. Description of global properties of solutions of functional-differential equations with state dependent deviation. In particular, existence and continuation of solutions, a structure of the set of complete solutions and asymptotic properties will be studied.
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