6533b861fe1ef96bd12c591f

RESEARCH PRODUCT

An abstract doubly nonlinear equation with a measure as initial value

Veli-matti HokkanenSergiu Aizicovici

subject

Differential equationApplied MathematicsMathematical analysisMonotonic functionNonlinear evolution equationMeasure (mathematics)Nonlinear systemMaximal monotone operatorProduct (mathematics)Bounded functionEvolution equationInitial value problemAnalysisMathematical physicsMathematics

description

Abstract The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A ( t ) x and B ( t ) x + C ( t ) x is bounded below.

yearjournalcountryeditionlanguage
2007-07-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2006.08.074