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Digitale Medien

Multiplicity results for asymptotically homogeneous semilinear boundary value problems (1986)

McKenna, P. J. ; Redlinger, Reinhard ; Walter, Wolfgang

Springer

Annali di matematica pura ed applicata 143 (1986), S. 247-257

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Details

ISSN: 1618-1891

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary This paper treats nonlinear elliptic boundary value problems of the form $$\Delta u + f(x,u) = 0in\Omega ,u = 0on\partial \Omega $$ in the spaceL 2(Ω) by degree theoretic methods. Emphasis is placed on existence of multiplesolutions in the case, where the nonlinearity f crosses several eigenvalues of the correspondingeigenvalue problem Δθ+λθ = 0 with zero boundary values. No differentiability conditions(but Lipschitz type conditions) on f are assumed. A main tool is a new a priori bound forsolutions (Theorem 1). The method is not confined to the selfadjoint case. It applies alsoto some time-periodic parabolic and hyperbolic problems.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01769219

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