Journal•ISSN: 0362-546X
Nonlinear Analysis-theory Methods & Applications
Elsevier BV
About: Nonlinear Analysis-theory Methods & Applications is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 0362-546X. Over the lifetime, 13837 publications have been published receiving 277544 citations. The journal is also known as: Theory, methods & applications & Nonlinear analysis, theory, methods and applications.
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TL;DR: On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x andu, Du) = 0 avec des conditions aux limites conormales et de Dirichlet.
Abstract: On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x,u,Du)=0 avec des conditions aux limites conormales et de Dirichlet
1,278 citations
TL;DR: In this paper, a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order was proved, using a weak contractivity type of assumption, which can be used to investigate a large class of problems.
Abstract: We prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order, using a weak contractivity type of assumption. Besides including several recent developments, our theorem can be used to investigate a large class of problems. As an application, we discuss the existence and uniqueness of solution for a periodic boundary value problem.
1,206 citations
TL;DR: In this article, the local C(1 + Alpha) nature of weak solutions of elliptic equations of the type (1.1) in the introduction under the degeneracy (or singularity) assumptions (A sub 1)-(A sub 3).
Abstract: : It is demonstrated the local C(1 + Alpha) nature of weak solutions of elliptic equations of the type (1.1) in the introduction under the degeneracy (or singularity) assumptions (A sub 1)-(A sub 3).
1,106 citations
TL;DR: In this article, it was shown that the inequalities analogous to (1.l) in either uniformly convex or uniformly smooth Banach spaces can be obtained for fixed points of uniformly Lipschitzian mappings and to best approximation theory.
Abstract: well known that many problems in a Hilbert space H are solved by applying the following identity: IlAx + (1 - A)YI12 = a412 + (1 - ~)llYl12 - A(1 - Mx - Yl12 (1.1) for all x, y in H and 0 5 I 5 1. Therefore, one natural method to solve problems in a Banach space Xis to establish equalities and (usually) inequalities in Xanalogous to (1.1). This is in fact shown by some authors’ recent work, see for example, Reich [l], Poffald and Reich [2], Lim [3], Lim et af. [4], Prus and Smarzewski [5], Smarzewski [6], and Reich [21]. The purpose of this paper is to continue carrying out investigations in this line. More precisely, in Section 3, we establish some inequalities analogous to (1 .l) in either uniformly convex or uniformly smooth Banach spaces. As corollaries, we obtain new characteristics of p-uniform convexity and q-uniform smoothness of a Banach space X via the functionals I] . lip and II * llq respectively. We give in Section 4 applications of the inequalities obtained in Section 3 to fixed points of uniformly Lipschitzian mappings and to best approximation theory.
1,096 citations
TL;DR: In this paper, the basic theory for the initial value problem of fractional differential equations involving Riemann-Liouville differential operators is discussed employing the classical approach, and the theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.
Abstract: In this paper, the basic theory for the initial value problem of fractional differential equations involving Riemann–Liouville differential operators is discussed employing the classical approach. The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.
1,035 citations