Existence theorems for parameter dependent weakly continuous operators with applications. (English) Zbl 07851984
Summary: The paper presents results on the solvability and parameter dependence for problems driven by weakly continuous potential operators with continuously differentiable and coercive potential. We provide a parametric version on the existence result to nonlinear equations involving coercive and weakly continuous operators. Applications address a variant of elastic beam equation.
MSC:
| 47H05 | Monotone operators and generalizations |
| 47J05 | Equations involving nonlinear operators (general) |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
weakly continuous operator; surjectivity; continuous dependence on parameters; beam equationReferences:
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