# An abstract nonlinear second order differential equation

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 2, page 155-166
- ISSN: 0066-2216

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topJan Bochenek. "An abstract nonlinear second order differential equation." Annales Polonici Mathematici 54.2 (1991): 155-166. <http://eudml.org/doc/262326>.

@article{JanBochenek1991,

abstract = {By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.},

author = {Jan Bochenek},

journal = {Annales Polonici Mathematici},

keywords = {semilinear differential equation in Banach space; Cauchy problem; nonlinear integral equation},

language = {eng},

number = {2},

pages = {155-166},

title = {An abstract nonlinear second order differential equation},

url = {http://eudml.org/doc/262326},

volume = {54},

year = {1991},

}

TY - JOUR

AU - Jan Bochenek

TI - An abstract nonlinear second order differential equation

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 2

SP - 155

EP - 166

AB - By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.

LA - eng

KW - semilinear differential equation in Banach space; Cauchy problem; nonlinear integral equation

UR - http://eudml.org/doc/262326

ER -

## References

top- [1] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
- [2] R. Rabczuk, Elements of the Theory of Differential Inequalities, PWN, Warszawa 1976 (in Polish). Zbl0351.34006
- [3] I. Segal, Nonlinear semi-groups, Ann. of Math. 78 (1963), 339-364. Zbl0204.16004
- [4] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96. Zbl0388.34039
- [5] T. Winiarska, Differential Equations with Parameter, Monograph 68, Technical University of Cracow, 1988.
- [6] K. Yosida, Functional Analysis, Springer, New York 1980.

## Citations in EuDML Documents

top- Jan Bochenek, An abstract semilinear first order differential equation in the hyperbolic case
- Jan Bochenek, Second order semilinear Volterra integrodifferential equation in Banach space
- Jan Bochenek, Teresa Winiarska, Second order evolution equations with parameter
- Sotiris K. Ntouyas, Panagiotis Ch. Tsamatos, Global existence for second-order functional semilinear integrodifferential equations
- P. Balasubramaniam, S.K. Ntouyas, Existence of solutions for second order stochastic differential inclusions in Hilbert spaces

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