- journal article metadata
European Mathematical Society Publishing House
2018-08-30 23:30:01
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
34
2018
3
Critical points of non-regular integral functionals
Lucio
Boccardo
Università di Roma La Sapienza, Italy
Benedetta
Pellacci
Università degli Studi della Campania "Luigi Vanvitelli", Caserta, Italy
Non-smooth critical point theory, quasi-linear Schrödinger equations, quadratic growth in the gradient
We prove the existence of a bounded positive critical point for a class of functionals such as $$J(v)=\frac12\int_o [a(x)+b(x)|v|^{\gamma}]\, |\nabla v|^{2}-\int_o |v|^{p}$$ for $\Omega$ a bounded open set in $\mathbb R^{N}$, $N>2$,$\gamma+2< p < 2N/(N-2)$, $\gamma>0$, $\gamma\neq 1$ and $a(x),\,b(x)$ measurable function satisfying $0
Partial differential equations
Ordinary differential equations
1001
1020
10.4171/RMI/1013
http://www.ems-ph.org/doi/10.4171/RMI/1013
8
27
2018