Advances in Differential Equations

Semilinear elliptic equations with sublinear indefinite nonlinearities

Stanley Alama

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Abstract

We prove existence, multiplicity and bifurcation results for a family of semilinear Neumann problems with nonlinear terms that are indefinite in sign and exhibit sublinear growth near zero. The solutions are non-negative, but the combined effect of indefiniteness and the non-Lipschitz character of the nonlinear term yields solutions which may vanish on large sets. Combining variational methods with bifurcation analysis and the sub- and super-solution

Article information

Source
Adv. Differential Equations, Volume 4, Number 6 (1999), 813-842.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366030748

Mathematical Reviews number (MathSciNet)
MR1729392

Zentralblatt MATH identifier
0952.35052

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 47J30: Variational methods [See also 58Exx] 58E07: Abstract bifurcation theory 92D40: Ecology

Citation

Alama, Stanley. Semilinear elliptic equations with sublinear indefinite nonlinearities. Adv. Differential Equations 4 (1999), no. 6, 813--842. https://projecteuclid.org/euclid.ade/1366030748


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