On weak solutions of functional-differential abstract nonlocal Cauchy problems

• Autorzy: Ludwik Byszewski
• Języki publikacji: EN

Abstrakty

EN

The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.

Słowa kluczowe

EN

abstract Cauchy problems; functional-differential equation; nonlocal conditions; weak solutions; existence; uniqueness; asympto tic stability; m-accretive operators; Banach contraction theorem

Kategorie tematyczne

• 47H06: Accretive operators, dissipative operators, etc.
• 34K30: Equations in abstract spaces
• 47H20: Semigroups of nonlinear operators
• 34K25: Asymptotic theory
• 34G20: Nonlinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 2
• Strony: 163-170

Daty

wydano

1997

otrzymano

1995-11-08

poprawiono

1996-06-15

Twórcy

autor

Ludwik Byszewski

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] J. Bochenek, An abstract semilinear first order differential equation in the hyperbolic case, Ann. Polon. Math. 61 (1995), 13-23.
• [2] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
• [3] L. Byszewski, Uniqueness criterion for solution of abstract nonlocal Cauchy problem, J. Appl. Math. Stochastic Anal. 6 (1993), 49-54.
• [4] L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, in: Selected Problems of Mathematics, Cracow University of Technology, Anniversary Issue 6 (1995), 25-33.
• [5] M. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57-94.
• [6] L. Evans, Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math. 26 (1977), 1-42.
• [7] A. Kartsatos, A direct method for the existence of evolution operators associated with functional evolutions in general Banach spaces, Funkcial. Ekvac. 31 (1988), 89-102.
• [8] A. Kartsatos and M. Parrott, A simplified approach to the existence and stability problem of a functional evolution equation in a general Banach space, in: Infinite Dimensional Systems, (F. Kappel and W. Schappacher (eds.), Lecture Notes in Math. 1076, Springer, Berlin, 1984, 115-122.
• [9] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339.
• [10] T. Winiarska, Regularity of solutions of parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 56 (1992), 311-317.