Advances in Differential Equations

Semilinear elliptic equations with sublinear indefinite nonlinearities

Stanley Alama

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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

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

First available in Project Euclid: 15 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Alama, Stanley. Semilinear elliptic equations with sublinear indefinite nonlinearities. Adv. Differential Equations 4 (1999), no. 6, 813--842.

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