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Exact(23)
Here ω is a weight function which may change sign and may vanish on a set of positive measure.
If, differently from Theorems 1 and 2, we have h(a + ) < 0 then h(x) may change sign once.
This paper studies the eigenvalue interval for the singular boundary value problem, where may be singular at, , and may change sign and be superlinear at.
To the best of our knowledge, there is little literature about nodal periodic solutions (that is, periodic solutions may change sign) except for some special cases.
Of course the natural question is: what would happen if we allow that the functions b and b ˆ may change sign?
In general, the thinner the double layer surrounding a drop and/or the longer its distance from a planar surface, the larger its mobility, and if a drop is sufficiently close to a plane, its mobility may change sign.
Similar(37)
In this paper, we are interested in Π p D ( a, b ) and Π p N ( a, b ), where the weights a, b ∈ L 1 [ 0, 1 ] are assumed to be indefinite (i.e., a and b may or may not change sign).
where is a constant and the associated Green's function may changes sign.
where is a constant and in which case the associated Green's function may changes sign.
The interesting point is that the nonlinear term f not only involve with the first-order and the second-order derivatives explicitly, but also may be allowed to change sign and may be singular at t = 0 and/or t = 1.
Note that in our problem, q may change its sign, so we call this type of problem semipositone.
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