On the existence of solutions to nonlinear equations involving singular mappings with non-zero \(p\)-kernel

DOI10.1007/s11228-011-0177-9zbMath1235.47054OpenAlexW2036553523MaRDI QIDQ645071

Agnieszka Prusińska, Alexey A. Tret'yakov

Publication date: 8 November 2011

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-011-0177-9

zbMATH Keywords

multivalued mapping\(p\)-regularity theorycontraction principle for multivalued mappingsnonlinear equation with singular mappings

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items

Existence of periodic solutions to nonlinear \(p\)-regular boundary value problem, Iterative method for solving nonlinear singular problems, \(p\)-regularity theory. Tangent cone description in the singular case, Implicit function and tangent cone theorems for singular inclusions and applications to nonlinear programming, Irregular optimization models and \(p\)-order Kuhn-Tucker optimality conditions, New versions of Newton method: step-size choice, convergence domain and under-determined equations

Cites Work

• Unnamed Item
• The \(p\)th order optimality conditions for nonregular optimization problems
• Factor-analysis of nonlinear mappings: \(p\)-regularity theory
• Solvability of the Cauchy problem for a first-order partial differential equation in the degenerate case
• A remark on the existence of solutions to nonlinear equations with degenerate mappings
• Multi-valued contraction mappings in generalized metric spaces
• Necessary and sufficient conditions for optimality of p-th order
• Optimality Conditions for Degenerate Extremum Problems with Equality Constraints
• The implicit function theorem in degenerate problems
• Methods for solving degenerate problems