Advances in Differential Equations

Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations

Filippo Gazzola and Bernhard Ruf

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The solvability of semilinear elliptic equations with nonlinearities in the critical growth range depends on the terms with lower-order growth. We generalize some known results to a wide class of lower-order terms and prove a multiplicity result in the left neighborhood of every eigenvalue of $-\Delta$ when the subcritical term is linear. The proofs are based on variational methods; to assure that the considered minimax levels lie in a suitable range, special classes of approximating functions having disjoint support with the Sobolev ``concentrating" functions are constructed.

Article information

Adv. Differential Equations, Volume 2, Number 4 (1997), 555-572.

First available in Project Euclid: 23 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B20: Perturbations


Gazzola, Filippo; Ruf, Bernhard. Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations. Adv. Differential Equations 2 (1997), no. 4, 555--572.

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