On the existence of multiple solutions for a nonlocal BVP with vector-valued response
The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.
Keywordsnonlocal boundary-value problems positive solutions duality method variational method
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- V. A. Il’in and E. I. Moiseev: Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differ. Equ. 23 (1987), 803–811.Google Scholar
- V. A. Il’in and E. I. Moiseev: Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differ. Equ. 23 (1987), 979–987.Google Scholar
- G. L. Karakostas and P. Ch. Tsamatos: Positive solutions of a boundary-value problem for second order ordinary differential equations. Electronic Journal of Differential Equations 49 (2000), 1–9.Google Scholar
- G. L. Karakostas and P. Ch. Tsamatos: Positive solutions for a nonlocal boundary-value problem with increasing response. Electronic Journal of Differential Equations 73 (2000), 1–8.Google Scholar
- M. A. Krasnoselski: Positive solutions of operator equations. Noordhoff, Groningen, 1964.Google Scholar
- R. Ma: Existence of positive solutions for second order m-point boundary value problems. Annales Polonici Mathematici LXXIX.3 (2002), 256–276.Google Scholar
- J. Mawhin: Problèmes de Dirichlet Variationnels Non Linéares. Les Presses de l’Université de Montréal (1987).Google Scholar
- P. H. Rabinowitz: Minimax Methods in Critical Points Theory with Applications to Differential Equations. AMS, Providence, 1986.Google Scholar
- M. Willem: Minimax Theorems. Progress in Nonlinear Differential Equations and Their Applications. Basel, Boston, Berlin: Birkhäuser, Vol. 24, 1996.Google Scholar