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Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

Józef Banaś (2012)

Open Mathematics

The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.

Méthodes opérationnelles dans l'étude des problèmes aux limites

Pierre Grisvard (1964/1966)

Séminaire Bourbaki

Mixed monotone iterative technique for abstract impulsive evolution equations in Banach spaces.

Yang, He (2010)

Journal of Inequalities and Applications [electronic only]

Monotone operators in divergence form with $x$ -dependent multivalued graphs

Gilles Francfort, François Murat, Luc Tartar (2004)

Bollettino dell'Unione Matematica Italiana

We prove the existence of solutions to $- div a (x, grad u) = f$ , together with appropriate boundary conditions, whenever $a (x, e)$ is a maximal monotone graph in $e$ , for every fixed $x$ . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a $45^{\circ}$ rotation, for every fixed $x$ ; in other words, the graph $d \in a (x, e)$ is defined through $d - e = φ (x, d + e)$ , where $φ$ is a Carathéodory contraction in $R^{N}$ . This definition is shown to be equivalent to the fact that $a (x, \cdot)$ is pointwise monotone...

Monotone positive solution of nonlinear third-order BVP with integral boundary conditions.

Sun, Jian-Ping, Li, Hai-Bao (2010)

Boundary Value Problems [electronic only]

Monotone positive solutions for $p$ -Laplacian equations with sign changing coefficients and multi-point boundary conditions.

Xia, Jianye, Liu, Yuji (2010)

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

Monotone technique for second order discontinuous differential inclusions.

Dhage, Bapurao C. (2006)

Applied Mathematics E-Notes [electronic only]

m-Point Boundary Value Problems

P. Ch. Tsamatos, Ch. P. Gupta, S. K. Ntouyas (2000)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Multi-bump ground states of the Gierer–Meinhardt system in R2

Manuel del Pino, Michał Kowalczyk, Juncheng Wei (2003)

Annales de l'I.H.P. Analyse non linéaire

Multiple nonnegative solutions for second-order boundary-value problems with sign-changing nonlinearities.

Xi, Shouliang, Jia, Mei, Ji, Huipeng (2009)

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

Multiple positive periodic solutions for delay differential system.

Hao, Zhao-Cai, Xiao, Ti-Jun, Liang, Jin (2009)

Discrete Dynamics in Nature and Society

Multiple positive solutions for a nonlinear 2n-th order m-point boundary value problems.

Wang, Youyu, Tang, Yantao, Zhao, Meng (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Multiple positive solutions for a nonlinear $3 n$ -th order three-point boundary-value problem.

Devi, K.L.Saraswathi, Prasad, Kapula R. (2010)

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

Multiple positive solutions for boundary value problems of second-order differential equations system on the half-line.

Xi, Shouliang, Jia, Mei, Ji, Huipeng (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Multiple positive solutions for impulsive singular boundary value problems with integral boundary conditions.

Li, Meiqiang, Feng, Xianggui, Xue, Chunyan (2009)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Multiple positive solutions for $m$ -point boundary value problem on time scales.

Liu, Jie, Sun, Hong-Rui (2011)

Boundary Value Problems [electronic only]

Multiple positive solutions for $(n - 1, 1)$ -type semipositone conjugate boundary value problems of nonlinear fractional differential equations.

Yuan, Chengjun (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Multiple positive solutions for $n$ th order multipoint boundary value problem.

Li, Yaohong, Wei, Zhongli (2010)

Boundary Value Problems [electronic only]

Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions

Abdelkader Belarbi, Mouffak Benchohra, Abdelghani Ouahab (2008)

Archivum Mathematicum

In this paper we investigate the existence of multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. We shall rely on the Leggett-Williams fixed point theorem.

Multiple positive solutions for nonlinear first-order impulsive dynamic equations on time scales with parameter.

Wang, Da-Bin, Guan, Wen (2009)

Advances in Difference Equations [electronic only]

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