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Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of positive solutions of the integral equation $x (t) = μ \int_{0}^{1} k (t, s) f (s, x (s), x^{'} (s), ..., x^{(n - 1)} (s)) d s, n \geq 2$ in both $C^{n - 1} [0, 1]$ and $W^{n - 1, p} [0, 1]$ spaces, where $p \geq 1$ and $μ > 0$ . Throughout this paper $k$ is nonnegative but the nonlinearity $f$ may take negative values. The Krasnosielski fixed point theorem on cone is used.

Remarks on Krasnoselskii bifurcation theorem

Raffaele Chiappinelli (1989)

Commentationes Mathematicae Universitatis Carolinae

Remarks on multiple periodic solutions of nonlinear ordinary differential equations

Pavel Drábek (1980)

Commentationes Mathematicae Universitatis Carolinae

Remarks on Nagumo's condition.

Korman, Ph. (1998)

Portugaliae Mathematica

Remarks on nonlinear noncoercive problems with jumping nonlinearities

Pavel Drábek (1984)

Commentationes Mathematicae Universitatis Carolinae

Remarks on periodic solvability of nonlinear ordinary differential equations

Milan Konečný (1977)

Commentationes Mathematicae Universitatis Carolinae

Remarks on semilinear problems with nonlinearities depending on the derivative.

Almira, Jose María, Del Toro, Naira (2003)

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

Remarks on Some Dirichlet Type Results for Semibounded Sturm-Liouville Operators.

Hubert Kalf (1974)

Mathematische Annalen

Remarks on some monotonicity conditions for the period function

R. Chouikha, F. Cuvelier (1999)

Applicationes Mathematicae

We are interested in the optimality of monotonicity criteria for the period function of some planar Hamiltonian systems. This study is illustrated by examples.

Remarks on some nonlinear boundary value problems

Svatopluk Fučík (1976)

Commentationes Mathematicae Universitatis Carolinae

Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities

Juan J. Nieto (1990)

Commentationes Mathematicae Universitatis Carolinae

Remarks on the uniqueness of radial solutions

J. Smoller, A. Wasserman (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Representation of the norming constants by two spectra.

Harutyunyan, Tigran N. (2010)

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

Reproducing kernel method for singular fourth order four-point boundary value problems.

Li, Xiuying, Wu, Boying (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Resolvent kernel for the Kohn Laplacian on Heisenberg groups.

Askour, Neur Eddine, Mouayn, Zouhair (2002)

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

Resonance and multiplicity in periodic boundary value problems with singularity

Irena Rachůnková, Milan Tvrdý, Ivo Vrkoč (2003)

Mathematica Bohemica

The paper deals with the boundary value problem $u^{''} + k u = g (u) + e (t), u (0) = u (2 π), u^{'} (0) = u^{'} (2 π),$ where $k \in ℝ$ , $g I \mapsto ℝ$ is continuous, $e \in 𝕃 J$ and ${lim}_{x \to 0 +} \int_{x}^{1} g (s) d s = \infty .$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.

Currently displaying 21 – 40 of 46

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Displaying 21 – 40 of 46

Remarks on existence of positive solutions of some integral equations

Remarks on Krasnoselskii bifurcation theorem

Remarks on multiple periodic solutions of nonlinear ordinary differential equations

Remarks on Nagumo's condition.

Remarks on nonlinear noncoercive problems with jumping nonlinearities

Remarks on periodic solvability of nonlinear ordinary differential equations

Remarks on semilinear problems with nonlinearities depending on the derivative.

Remarks on Some Dirichlet Type Results for Semibounded Sturm-Liouville Operators.

Remarks on some monotonicity conditions for the period function

Remarks on some nonlinear boundary value problems

Remarks on some nonlinear Dirichlet problems with unbounded nonlinearities

Remarks on the uniqueness of radial solutions

Representation of the norming constants by two spectra.

Reproducing kernel method for singular fourth order four-point boundary value problems.

Resolvent kernel for the Kohn Laplacian on Heisenberg groups.

Resonance and multiplicity in periodic boundary value problems with singularity

Resonance and nonresonance periodic value problems of first-order differential systems.

Resonant problem for a class of bvps on the half-line.

Resonant problem for some second-order differential equation on the half-line.

Results for twin singular nonlinear problems with damping term.

Currently displaying 21 – 40 of 46