Abstract
In this paper we are concerned with the existence and multiplicity of radial solutions to the BVP
whereB is an open ball in ℝK and u↦∇·(a(|∇u|)∇u) is a nonlinear differential operator (e.g. the plaplacian or the mean curvature operator). The function f is defined in a neighborhood of u=0 and satisfies a «sublinear»-type growth condition for u→0. We use a degree approach combined with a time-map technique. Multiplicity results are obtained also for nonlinearities of concave-convex type.
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Dedicated to Professor Tongren Ding on the occasion of his 70th birthday
Entrata in Redazione il 16 marzo 1999.
Under the auspices of GNAFA-C.N.R., Italy. Work performed in the frame of the EEC project “Nonlinear boundary value problems: existence, multiplicity and stability of solutions», grant CHRX-CT94-0555.
Partially supported by I.N.d.A.M., Italy.
Supported by EC project «Some nonlinear boundary value problems for differential equations», grant CI1*-CT93-0323 and by MURST 40% «Metodi ed applicazioni di equazioni differenziali ordinarie».
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Capietto, A., Dambrosio, W. & Zanolin, F. Infinitely many radial solutions to a boundary value problem in a ball. Annali di Matematica pura ed applicata 179, 159–188 (2001). https://doi.org/10.1007/BF02505953
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DOI: https://doi.org/10.1007/BF02505953