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https://doi.org/10.3336/gm.48.2.11

Quasilinear elliptic equations with positive exponent on the gradient

Jadranka Kraljević ; Faculty of Economics, University of Zagreb, Kennedyev trg 6, 10000 Zagreb, Croatia
Darko Žubrinić ; Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia


Puni tekst: engleski pdf 148 Kb

str. 391-402

preuzimanja: 360

citiraj


Sažetak

We study the existence and nonexistence of positive, spherically symmetric solutions of a quasilinear elliptic equation (1.1) involving p-Laplace operator, with an arbitrary positive growth rate e0 on the gradient on the right-hand side. We show that e0=p-1 is the critical exponent: for e0< p-1 there exists a strong solution for any choice of the coefficients, which is a known result, while for e0>p-1 we have existence-nonexistence splitting of the coefficients and . The elliptic problem is studied by relating it to the corresponding singular ODE of the first order. We give sufficient conditions for a strong radial solution to be the weak solution. We also examined when ω-solutions of (1.1), defined in Definition 2.3, are weak solutions. We found conditions under which strong solutions are weak solutions in the critical case of e0=p-1.

Ključne riječi

Quasilinear elliptic; positive strong solution; ω-solution; critical exponent; existence; nonexistence; weak solution

Hrčak ID:

112215

URI

https://hrcak.srce.hr/112215

Datum izdavanja:

16.12.2013.

Posjeta: 849 *