Integral equations of the first kind of Sonine type.

Samko, Stefan G.; Cardoso, Rogério P.

Displaying similar documents to “Integral equations of the first kind of Sonine type.”

Exponential stability of two coupled second-order evolution equations.

Wan, Qian, Xiao, Ti-Jun (2011)

Advances in Difference Equations [electronic only]

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Existence of solutions for a class of second-order $p$ -Laplacian systems with impulsive effects

Peng Chen, Xianhua Tang (2014)

Applications of Mathematics

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The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system $\begin{matrix} \frac{d}{d t} (| \dot{u} (t) |^{p - 2} \dot{u} (t)) = \nabla F (t, u (t)), a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0, \\ Δ {\dot{u}}^{i} (t_{j}) = {\dot{u}}^{i} (t_{j}^{+}) - {\dot{u}}^{i} (t_{j}^{-}) = I_{i j} (u^{i} (t_{j})), i = 1, 2, \dots, N; j = 1, 2, \dots, m . \end{matrix}$ By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$ -Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.

Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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Existence results are established for the resonant problem $y^{''} + λ_{m} a y = f (t, y)$ a.e. on $[0, 1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a \in L_{l o c}^{1} (0, 1)$ with $a > 0$ a.e. on $[0, 1]$ and $\int_{0}^{1} x (1 - x) a (x) d x < \infty$ .