EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS

Gennaro Infante

doi:10.1017/S0013091501001079

Abstract

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Working on a suitable cone of continuous functions, we give new results for integral equations of the form $\lambda u(t)=\int_{G}k(t,s)f(s,u(s))\,\mathrm{d} s:=Tu(t)$, where $G$ is a compact set in $\mathbb{R}^{n}$ and $k$ is a possibly discontinuous function that is allowed to change sign. We apply our results to prove existence of eigenvalues of some non-local boundary-value problems.

AMS 2000 Mathematics subject classification: Primary 34B10. Secondary 34B18; 47H10; 47H30

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Yang, Zhilin 2005. Positive solutions to a system of second-order nonlocal boundary value problems. Nonlinear Analysis: Theory, Methods & Applications, Vol. 62, Issue. 7, p. 1251.

Lan, K.Q. 2006. Multiple eigenvalues for singular Hammerstein integral equations with applications to boundary value problems. Journal of Computational and Applied Mathematics, Vol. 189, Issue. 1-2, p. 109.

Yang, Zhilin 2006. Positive solutions of a second-order integral boundary value problem. Journal of Mathematical Analysis and Applications, Vol. 321, Issue. 2, p. 751.

Franco, Daniel Infante, Gennaro and O’regan, Donal 2006. Positive and Nontrivial Solutions for the Urysohn Integral Equation. Acta Mathematica Sinica, English Series, Vol. 22, Issue. 6, p. 1745.

Sun, Yongping 2007. Optimal existence criteria for symmetric positive solutions to a three-point boundary value problem. Nonlinear Analysis: Theory, Methods & Applications, Vol. 66, Issue. 5, p. 1051.

Henderson, J. and Ntouyas, S. K. 2007. Positive solutions for systems of nonlinear eigenvalue problems for functional differential equations. Applicable Analysis, Vol. 86, Issue. 11, p. 1365.

Pečiulytė, Sigita and Štikonas, Artūras 2007. ON POSITIVE EIGENFUNCTIONS OF STURM-LIOUVILLE PROBLEM WITH NONLOCAL TWO‐POINT BOUNDARY CONDITION. Mathematical Modelling and Analysis, Vol. 12, Issue. 2, p. 215.

Sun, Yongping 2007. Existence and multiplicity of symmetric positive solutions for three-point boundary value problem. Journal of Mathematical Analysis and Applications, Vol. 329, Issue. 2, p. 998.

Henderson, Johnny Ntouyas, Sotiris K. and Purnaras, Ioannis K. 2008. POSITIVE SOLUTIONS FOR SYSTEMS OF M‐POINT NONLINEAR BOUNDARY VALUE PROBLEMS. Mathematical Modelling and Analysis, Vol. 13, Issue. 3, p. 357.

Pei, Minghe and Chang, Sung Kag 2008. The generalized quasilinearization method for second-order three-point boundary value problems. Nonlinear Analysis: Theory, Methods & Applications, Vol. 68, Issue. 9, p. 2779.

Sun, Yong-ping 2008. Monotone positive solution for three-point boundary value problem. Applied Mathematics-A Journal of Chinese Universities, Vol. 23, Issue. 3, p. 279.

Purnaras, I.K. 2009. On the existence of nonnegative solutions to an integral equation with applications to boundary value problems. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 9, p. 3914.

Štikonas, Artūras and Štikonienė, Olga 2009. CHARACTERISTIC FUNCTIONS FOR STURM—LIOUVILLE PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS. Mathematical Modelling and Analysis, Vol. 14, Issue. 2, p. 229.

Roman, S. and Štikonas, A. 2009. Green’s functions for stationary problems with nonlocal boundary conditions. Lithuanian Mathematical Journal, Vol. 49, Issue. 2, p. 190.

Jachimavičienė, J. Jesevičiūtė, Ž. and Sapagovas, M. 2009. The Stability of Finite-Difference Schemes for a Pseudoparabolic Equation with Nonlocal Conditions. Numerical Functional Analysis and Optimization, Vol. 30, Issue. 9-10, p. 988.

Graef, John R. and Moussaoui, Toufik 2009. A class of nth-order BVPs with nonlocal conditions. Computers & Mathematics with Applications, Vol. 58, Issue. 8, p. 1662.

Štikonas, A. and Roman, S. 2009. Stationary Problems with Two Additional Conditions and Formulae for Green's Functions. Numerical Functional Analysis and Optimization, Vol. 30, Issue. 9-10, p. 1125.

Yang, Chuan-Fu 2010. INVERSE NODAL PROBLEM FOR A CLASS OF NONLOCAL STURM‐LIOUVILLE OPERATOR. Mathematical Modelling and Analysis, Vol. 15, Issue. 3, p. 383.

Rao, A. Kameswara and Rao, S. Nageswara 2011. POSITIVE SOLUTIONS FOR ITERATIVE SYSTEMS OF NONLINEAR BOUNDARY VALUE PROBLEMS ON TIME SCALES. Asian-European Journal of Mathematics, Vol. 04, Issue. 01, p. 95.

Liang, Jitai Liu, Yiliang and Liu, Zhenhai 2011. A class of BVPS for first order impulsive integro-differential equations. Applied Mathematics and Computation, Vol. 218, Issue. 7, p. 3667.

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EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS

Abstract

Keywords

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