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New conditions for the existence of non trivial solutions to some Volterra equations.

W. Okrasinski (1990)

Extracta Mathematicae

We consider the following Volterra equation:(1) u(x) = ∫0x k(x-s) g(u(s)) ds, where,k: [0, δ0] → R is an increasing absolutely continuous function such thatk(0) = 0g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]).Let us note that (1) has always the trivial solution u = 0.Some necessary and sufficient conditions for the existence of nontrivial solutions to (1) with k(x) = xα - 1 (α>0) are given in [1], [2] and...

New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations

Espedito De Pascale, Pjotr P. Zabrejko (1998)

Rendiconti del Seminario Matematico della Università di Padova

New retarded integral inequalities with applications.

Agarwal, Ravi P., Kim, Young-Ho, Sen, S.K. (2008)

Journal of Inequalities and Applications [electronic only]

Non-autonomous implicit integral equations with discontinuous right-hand side

Giovanni Anello, Paolo Cubiotti (2004)

Commentationes Mathematicae Universitatis Carolinae

We deal with the implicit integral equation $h (u (t)) = f (t, \int_{I} g (t, z) u (z) d z) for a.a. t \in I,$ where $I : = [0, 1]$ and where $f : I \times [0, λ] \to ℝ$ , $g : I \times I \to [0, + \infty [$ and $h :] 0, + \infty [\to ℝ$ . We prove an existence theorem for solutions $u \in L^{s} (I)$ where the contituity of $f$ with respect to the second variable is not assumed.

Non-autonomous vector integral equations with discontinuous right-hand side

Paolo Cubiotti (2001)

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation $u (t) = f (t, \int_{I} g (t, z) u (z) d z)$ , with $t \in I : = [0, 1]$ , $f : I \times ℝ^{n} \to ℝ^{n}$ and $g : I \times I \to [0, + \infty [$ . We prove an existence theorem for solutions $u \in L^{s} (I, ℝ^{n})$ , $s \in] 1, + \infty]$ , where $f$ is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where $f$ does not depend explicitly on the first variable $t \in I$ .

Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales.

Janno, J. (1999)

Zeitschrift für Analysis und ihre Anwendungen

Nonlinear hyperbolic equations with dissipative temporal and spatial non-local memory.

Mošna, F., Nečas, J. (1999)

Zeitschrift für Analysis und ihre Anwendungen

Nonlinear impulsive Volterra integral equations in Banach spaces and applications.

Guo, Dajun (1993)

Journal of Applied Mathematics and Stochastic Analysis

Nonlinear integrodifferential equations of mixed type in Banach spaces.

Sikorska-Nowak, Aneta, Nowak, Grzegorz (2007)

International Journal of Mathematics and Mathematical Sciences

Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

Haribhau L. Tidke, Machindra B. Dhakne (2012)

Applications of Mathematics

The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.

Nonlinear Volterra Equations With Infinite Delay.

W.E. Fitzgibbon (1977)

Monatshefte für Mathematik

Nonlinear Volterra integral equation of the second kind and biorthogonal systems.

Berenguer, M.I., Gámez, D., Garralda-Guillem, A.I., Pérez, M.C.Serrano (2010)

Abstract and Applied Analysis

Nonlocal Cauchy problem for quasilinear integrodifferential equations in Banach spaces.

Chandrasekaran, Mariappan (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.

Nonnegative solutions of nonlinear integral equations

Michal Fečkan (1995)

Commentationes Mathematicae Universitatis Carolinae

Existence results of nonnegative solutions of asymptotically linear, nonlinear integral equations are studied.

Non-negative solutions of some non-linear integral equations

Wojciech Okrasiński (1984)

Annales Polonici Mathematici

Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces.

Guo, Dajun (1991)

Journal of Applied Mathematics and Stochastic Analysis

Currently displaying 1 – 20 of 26

Page 1 Next

Displaying 1 – 20 of 26

New conditions for the existence of non trivial solutions to some Volterra equations.

New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations

New retarded integral inequalities with applications.

Non-autonomous implicit integral equations with discontinuous right-hand side

Non-autonomous vector integral equations with discontinuous right-hand side

Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales.

Nonlinear hyperbolic equations with dissipative temporal and spatial non-local memory.

Nonlinear impulsive Volterra integral equations in Banach spaces and applications.

Nonlinear integrodifferential equations of mixed type in Banach spaces.

Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

Nonlinear Volterra Equations With Infinite Delay.

Nonlinear Volterra integral equation of the second kind and biorthogonal systems.

Nonlocal Cauchy problem for quasilinear integrodifferential equations in Banach spaces.

Nonnegative solutions of a class of second order nonlinear differential equations

Nonnegative solutions of nonlinear integral equations

Non-negative solutions of some non-linear integral equations

Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces.

Nonnegative solutions to an integral equation and its applications to systems of boundary value problems.

Note on some integral Volterra equations.

N-th order impulsive integro-differential equations in Banach spaces.

Currently displaying 1 – 20 of 26