Existence of a positive solution for a second order Sturm-Liouville boundary value problem on the half-line with a nonlinear derivative dependence via variational methods
Résumé
In this paper, a class of second order Sturm-Liouville boundary value problem on the half-line with dependence derivative is considered. The existence of a positive classical solution is proved by using variational methods and iterative methods.
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Références
R. P. Agarwal, Huei-Lin Hong and Cheh-Chih Yeh., The existence of positive solutions for the Sturm-Liouville boundary value problems. Comp. Math. Appl. 35, 89-96, (1998).
V. Anuradha, D. D. Hai and R. Shivaji., Existence results for superlinear semi-positive BVP’s, Proc. Amer. Math. Soc. 124, 757-763, (1996).
D. Averna and G. Bonanno., Three solutions for a quasilinear two point boundary value problem involving the onedimensional p-Laplacian, Proc. Edinburgh Math. Soc. 47, 257-270, (2004).
G. Bonanno and R. Livrea., Multiplicity theorems for the Dirichlet problem involving the p-Laplacian, Nonlinear Anal. 54, 1-7, (2003).
G. Bonanno., Existence of three solutions for a two point boundary value problem, Appl. Math. Letters. 13, 53-57, (2000).
Corduneanu, C., Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
L. H. Erbe and H. Wang., On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120, 743-748, (1994).
D. D. Figueiredo, M. Girardi and M. Matzeu., Semilinear elliptic equations with dependence on the gradient via mountain–pass techniques, Differential and Integral Equations. Volume 17. Numbers 1-2, 119-126, (2004).
W. Ge and J. Ren., New existence theorems of positive solutions for Sturm-Liouville boundary value problems, Appl. Math. Comput. 148, 631-644, (2004).
Mawhin, J and Willem, M., Critical point theory and Hamiltonian systems, Springer-Verlag, Berlin, 1989.
Y. Tian and W. Ge., Multiple positive solutions for a second order Sturm-Liouville boundary value problem with a p-Laplacian via variational methods, Rocky Mountain J. Math. 39, 325-342, (2009).
Y. Tian and W. Ge., Second-Order Sturm-Liouville boundary value problem involving the one-dimensional p-Laplacian, Rocky Mountain J. Math. 38, 309-327, (2008).
Zeidler, E., Nonlinear Functional Analysis and its Applications, Vol. III, Variational Methods and Applications, Springer, New York, 1985.
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