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Positive solutions of a renewal equation

100%

Traple J.

Annales Polonici Mathematici

1992

tom 57

nr 1

91-97

An existence theorem is proved for the scalar convolution type integral equation $x(t) = ∫_{-∞}^{∞} h(t - s)f(s,x(s))ds$.

Existence theorem for the Hammerstein integral equation

80%

Cichoń M., Kubiaczyk I.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1996

tom 16

nr 2

171-177

In this paper we prove an existence theorem for the Hammerstein integral equation $x(t) = p(t) + λ ∫_I K(t,s)f(s,x(s))ds$, where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

51%

Berdyshev A., Karimov E.

Open Mathematics

2006

tom 4

nr 2

183-193

In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Open Mathematics

1 Berdyshev A.

1 Cichoń M.

1 Karimov E.

1 Kubiaczyk I.

1 Traple J.

1 2006

1 1996

1 1992

Wyniki wyszukiwania

Positive solutions of a renewal equation

Existence theorem for the Hammerstein integral equation

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type