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Zbl 0793.35028
Díaz, G.; Letelier, R.
Explosive solutions of quasilinear elliptic equations: Existence and uniqueness. (English)
[J] Nonlinear Anal., Theory Methods Appl. 20, No.2, 97-125 (1993). ISSN 0362-546X

This paper deals with the quasilinear elliptic equation $$-\text {div} \biggl( Q \bigl( \vert \nabla u \vert \bigr) \nabla u \biggr)+\lambda \beta (u)=f \quad \text {in } \Omega \subset \bbfR\sp N,\ N>1;$$ more precisely, existence and uniqueness of local solutions satisfying $$u(x) \to \infty \quad \text {as dist} (x,\partial \Omega) \to 0$$ and other properties are the main goals here. These kinds of functions are called explosive solutions. No behaviour at the boundary to be prescribed is a priori imposed. However, we are going to show that, under an adequate strong interior structure condition on the equation, explosive behaviour near $\partial \Omega$ cannot be arbitrary. In fact, there exists a unique such singular character governed by a uniform rate of explosion depending only on the terms $Q$, $\lambda$, $\beta$ and $f$.

MSC 2000:: *35J60 Nonlinear elliptic equations
35B40 Asymptotic behavior of solutions of PDE

Keywords: nonlinear elliptic equations; explosive solutions; interior bounds; existence; uniqueness

Cited in: Zbl 0802.35076

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