Boundary Value Problems for Nonlinear Elliptic Equations with Two Parameters

被引：2

作者：

Felipe-Sosa R. ^{[1
]}

Felipe R. ^{[2
]}

机构：

[1] ICIMAF, Havana, Calle E esquina a 15, No. 309, Vedado

[2] CIMAT, Callejón Jalisco s/n Mineral de Valenciana, Guanajuato, Gto

来源：

Differential Equations and Dynamical Systems | 2014年 / 22卷 / 1期

关键词：

Elliptic nonlinear equations; Maximum Principle; Order Banach spaces;

D O I：

10.1007/s12591-013-0187-1

中图分类号：

学科分类号：

摘要：

We study the spectrum in ℝ2 of nonlinear elliptic equations with two parameters under certain boundary conditions. We use the Amanns method of finding the solutions of these equations as fixed points of functions defined on certain Order Banach Spaces of functions. Unlike the case studied by Amann, in the new situation the functions depend on two parameters and so the spectrum is a subset of ℝ2. © 2013 Foundation for Scientific Research and Technological Innovation.

引用

页码：1 / 13

页数：12

共 10 条

[1]

Amann H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, 4, pp. 620-709, (1976)

[2]

Caldwell S., Castro A., Shivaji R., Unsurangsie S., Positive solutions for classes of multiparameter elliptic semipositone problems, Electron. J. Differ. Equ., 2007, 96, pp. 1-10, (2007)

[3]

Hung K.-C., Wang S.-H., A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities, J. Math. Anal. Appl., 291, pp. 128-153, (2004)

[4]

Keller H.B., Cohen D.S., Some positone problems suggested by nonlinear heat generation, J. Math. Mech., 16, 12, pp. 1361-1376, (1967)

[5]

Krasnosel'skii M.A., Positive Solutions of Operator Equations, (1964)

[6]

Pao C.V., Nonlinear Parabolic and Elliptic Equations, (1992)

[7]

Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, (1967)

[8]

Schaefer H.H., Topological Vector Spaces. Graduate Texts in Mathematics, (1971)

[9]

Trejo I., Felipe R., The spectrum in ℝ and ℝ<sup>2</sup> of nonlinear elliptic equations with positive parameters, Rocky Mt. J. Math.

[10]

Wang F., An Y., Existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system, J. Math. Anal. Appl., 349, pp. 30-42, (2009)

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