Generalizations of Browder's Degree Theory
Copyright policy )Generalizations of Browder's Degree Theory
The starting point of this paper is the recent important work of F. E. Browder, who extended degree theory to operators of monotone type. The degree function of Browder is generalized to maps of the form T + f + G T + f + G , where T T is maximal monotone, f f is of class ( S ) + {(S)_ + } bounded, and G ( ⋅ ) G( \cdot ) is an u.s.c. compact multifunction. It is also generalized to maps of the form f + N G f + {N_G} , with f f of class ( S ) + {(S)_ + } and N G {N_G} the Nemitsky operator of a multifunction G ( x , r ) G(x,r) satisfying various types of sign conditions. Some examples are also included to illustrate the abstract results.
additivity on domain, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Degree theory for nonlinear operators, operators of monotone type, degree theory, sign condition, Nemitsky operator, compact multifunction, PDEs with multivalued right-hand sides, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), homotopy invariance, normalization, Nonlinear boundary value problems for linear elliptic equations, operator of class \((S)_ +\), compact embedding, Monotone operators and generalizations, approximate selector
additivity on domain, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Degree theory for nonlinear operators, operators of monotone type, degree theory, sign condition, Nemitsky operator, compact multifunction, PDEs with multivalued right-hand sides, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), homotopy invariance, normalization, Nonlinear boundary value problems for linear elliptic equations, operator of class \((S)_ +\), compact embedding, Monotone operators and generalizations, approximate selector
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