Surjectivity of an operator. (English) Zbl 0739.47030
Summary: A new method of proving surjectivity of an operator \(f\) in a Banach space is proposed. For this method the condition of coercivity of \(f\) in the form \(\lim_{| x|\to\infty}| f(x)|=\infty\) plays an important role. Some results obtained by this method deal with the strict surjective maps and with the quasi-bounded operators. The application of the results to ordinary differential equations is given.
MSC:
| 47J05 | Equations involving nonlinear operators (general) |
| 47H10 | Fixed-point theorems |
| 34G20 | Nonlinear differential equations in abstract spaces |
Keywords:
surjectivity of an operator; coercivity; strict surjective maps; quasi- bounded operators; ordinary differential equationsReferences:
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