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Entire large solutions of semilinear elliptic equations of mixed type

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  • We prove existence and nonexistence of nonnegative entire large solutions for the semilinear elliptic equation $\Delta u = p(x)f(u) + q(x)g(u)$ in which $f$ and $g$ are nondecreasing and vanish at the origin. The locally Hölder continuous functions $p$ and $q$ are nonnegative. We extend results previously obtained for special cases of $f$ and $g$.
    Mathematics Subject Classification: Primary: 35J25, 35J60; Secondary: 35B05, 34B18.

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