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Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign. (English) Zbl 1235.34064
The authors study criteria for the existence of a maximum or anti-maximum principle of a general second order operator with periodic conditions and conditions for non-resonance.

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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[2] Cabada, A.; Cid, J. A.: On the sign of the Green’s function associated to Hill’s equation with an indefinite potential, Appl. math. Comput. 205, 303-308 (2008) · Zbl 1161.34014 · doi:10.1016/j.amc.2008.08.008
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[11] Torres, P. J.: Existence of one -- signed periodic solutions of some second -- order differential equations via a Krasnoselskii fixed point theorem, J. differential equations 190, 643-662 (2003) · Zbl 1032.34040 · doi:10.1016/S0022-0396(02)00152-3
[12] Torres, P. J.: Weak singularities May help periodic solutions to exist, J. differential equations 232, 277-284 (2007) · Zbl 1116.34036 · doi:10.1016/j.jde.2006.08.006
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