×

zbMATH — the first resource for mathematics

A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\). (English) Zbl 0708.34019
The authors consider the boundary value problem \((\phi_ p(u'))'+f(t,u)=0,\) \(u(0)=u(T)=0\), where \(f: [0,1]\times {\mathbb R}\to {\mathbb R}\) is continuous and \(\phi_ p(s)=| s|^{p-2}s,\) \(p>1\). The problem stated is investigated by means of the Leray-Schauder homotopy method.
Reviewer: V.G.Angelov

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Boccardo, L.; Drábek, P.; Giachetti, D.; Kucera, M., Generalization of Fredholm alternative for nonlinear differential operators, Nonlinear anal., 10, 1083-1103, (1986) · Zbl 0623.34031
[2] Brezis, H., Analyse fonctionnelle, (1983), Masson Paris · Zbl 0511.46001
[3] \scM. del Pino, Applied Math. Engineering thesis, FCFM, Univ. of Chile.
[4] \scM. del Pino, M. Elgueta, and R. Manasevich, Sturm’s comparison theorem and a Hartman’s type oscillation criterion for \((¦u′¦\^{}\{p − 2\}u′)′ + c(t) ¦u¦\^{}\{p − 2\}u = 0\), preprint.
[5] Drábek, P., Ranges of a-homogeneous operators and their perturbations, C̃asopis Pěst. mat., 105, 167-183, (1980) · Zbl 0427.47048
[6] Fucik, S.; Kufner, A., Nonlinear differential equations, (1980), Elsevier Amsterdam/New York · Zbl 0647.35001
[7] Mawhin, J.; Ward, J.R., Nonresonance and existence for nonlinear elliptic B.V.P., Nonlinear anal. TMA, 6, (1981) · Zbl 0475.35047
[8] Mawhin, J.; Ward, J.R.; Willem, Variational methods and semilinear elliptic equations, Arch. rational mech. anal., 95, 264-277, (1986) · Zbl 0656.35044
[9] Rabinowitz, P., Théorie du degré topologique et applications a des problems aux limites non linéaires, (1975), Paris VI et CNRS
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.