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Poisson-Boltzmann equation in ℝ³

100%

Krzywicki A., Nadzieja T.

Annales Polonici Mathematici

1991

tom 54

nr 2

125-134

The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_{∂Ω} = 0$. One studies the existence of a solution of the problem and its properties.

Differential equations in banach space and henstock-kurzweil integrals

80%

Kubiaczyk I., Sikorska A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1999

tom 19

nr 1-2

35-43

In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.

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Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals

70%

Sikorska-Nowak A.

Commentationes Mathematicae

2007

tom 47

nr 2

We prove an existence theorems for the nonlinear integral equation \[ x(t) = f (t) + \int_{0}^a k_1 (t, s)x(s)ds + \int_{0}^a k_2(t, s)g(s, x(s))ds,\quad t \in I_a = [0, a], a \in \mathbb{R} _+, \] where $f, g, x$ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Commentationes Mathematicae

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Krzywicki A.

1 Kubiaczyk I.

1 Nadzieja T.

1 Sikorska A.

1 Sikorska-Nowak A.

1 2007

1 1999

1 1991

Wyniki wyszukiwania

Poisson-Boltzmann equation in ℝ³

Differential equations in banach space and henstock-kurzweil integrals

Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals