On the existence of solutions of operator differential equations
We consider nonlinear equations of parabolic type in reflexive Banach spaces. We present sufficient conditions for the existence of solutions of these equations. We use methods for the investigation of problems with operators of pseudomonotone (on a subspace) type. In addition, a sufficient criterion in the Sobolev space L p (0, T; W p 1 (Ω)∩L 2 (0, T; L2(Ω)) is considered for the case where an operator introduced with the use of functional coefficients belongs to a given class. We also show that it is possible to weaken the classical condition of coerciveness.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 6, pp 996-1014.
Citation Example: Solonukha O.V. On the existence of solutions of operator differential equations // Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 837–850.