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The negative numbers were sometimes seen as even more problematic, and in many cases negative solutions of equations were still considered by many to be "absurd" or "devoid of interest".
Then, u 3 and u 4 are negative solutions of BVP (1.1), (1.2).
Moreover, we can also obtain the existence of negative solutions of (1.1) and (1.2).
Theorem 1.1 establishes the existence of positive and negative solutions of (1.1) near ν 1.
In particular, Yuan and Cheung (see [26]) gave the negative solutions of (L_{p} -Busemann-Petty probL_{p} -Busemann-Petty
By Lemmas 3.6-3.8 3.6-3.8orem 2.1 in [17], there and Theoremitive and two negative solutions of problem (1.1).
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In case is a frequently negative solution of (1.6), then.
A similar argument gives a negative solution of system (1.1).
The existence of the greatest negative solution of (1.1) within can be proved similarly.
Finally, we assume that x is an eventually negative solution of (1.1).
Then {v n } is a negative solution of inequality (2.25), a contradiction.
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