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Multiple positive solutions for singular BVPs on the positive half-line. (English) Zbl 1142.34316
Summary: We are concerned with the existence of multiple positive solutions to a second-order nonlinear singular boundary value problem set on the positive half-line. We mainly use the Krasnozels’kĭi and Leggett-Williams fixed point theorems in cones to prove existence of one positive solution, two positive solutions and three positive solutions. The results complement, extend and correct some recent ones.

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
Full Text: DOI
[1] Djebali, S.; Moussaoui, T., A class of second order BVPs on infinite intervals, Electron. J. qual. theory differ. equ., 4, 1-19, (2006) · Zbl 1134.34018
[2] Hao, Z.-C.; Liang, J.; Xiao, T.-J., Positive solutions of operator equations on half-line, J. math. anal. appl., 314, 423-435, (2006) · Zbl 1086.47035
[3] Przeradzki, B., Travelling waves for reaction – diffusion equations with time depending nonlinearities, J. math. anal. appl., 281, 164-170, (2003) · Zbl 1032.35089
[4] Zima, M., On positive solutions of boundary value problems on the half-line, J. math. anal. appl., 259, 127-136, (2001) · Zbl 1003.34024
[5] Bielecki, A., Une remarque sur la Méthode de Banach-cacciopoli-Tikhonov dans la théorie des équations différentielles ordinaires, Bull. acad. Pol. sci., 4, 261-264, (1956) · Zbl 0070.08103
[6] Djebali, S.; Mebarki, K., Existence results for a class of BVPs on the positive half-line, Comm. appl. nonlinear anal., 14, 2, 13-31, (2007) · Zbl 1129.34017
[7] Agarwal, R.A.; Meehan, M.; O’Regan, D., Fixed point theory and applications, Cambridge tracts in mathematics, vol. 141, (2001), Cambridge University Press
[8] Krasnozels’kĭi, M.A., Positive solutions of operator equations, (1964), Noordhoff, Groningen The Netherlands
[9] Leggett, R.W.; Williams, L.R., Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana univ. math. J., 28, 673-688, (1979) · Zbl 0421.47033
[10] Meehan, M.; O’Regan, D., Existence theory for nonlinear Fredholm and Volterra integral equations on half open intervals, Nonlinear anal., 35, 355-387, (1999) · Zbl 0920.45006
[11] Zima, K., Sur l’existence des solutions d’une équation intégro-différentielle, Ann, polon. math. XXVII, 181-187, (1973) · Zbl 0257.45009
[12] Zima, M., On a certain boundary value problem, Annales societas mathematicae polonae. series I: comment. math. XXIX, 331-340, (1990) · Zbl 0724.34029
[13] Deimling, K., Nonlinear functional analysis, (1985), Springer-Verlag Berlin, Heidelberg · Zbl 0559.47040
[14] Guo, D.J.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press · Zbl 0661.47045
[15] Zeidler, E., Nonlinear functional analysis and its applications. vol. I: fixed point theorems, (1986), Springer-Verlag New York
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