The Dirichlet problem with sublinear nonlinearities
Aleksandra Orpel
Annales Polonici Mathematici, Tome 79 (2002), p. 131-140 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We investigate the existence of solutions of the Dirichlet problem for the differential inclusion 0∈Δx(y)+∂xG(y,x(y)) for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional J(x)=∫Ω1/2|∇x(y)|²-G(y,x(y))dy. We develop a duality theory and formulate the variational principle for this problem. As a consequence of duality, we derive the variational principle for minimizing sequences of J. We consider the case when G is subquadratic at infinity.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:280968 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-4,
     author = {Aleksandra Orpel},
     title = {The Dirichlet problem with sublinear nonlinearities},
     journal = {Annales Polonici Mathematici},
     volume = {79},
     year = {2002},
     pages = {131-140},
     zbl = {0997.58005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-4}
}

Aleksandra Orpel. The Dirichlet problem with sublinear nonlinearities. Annales Polonici Mathematici, Tome 79 (2002) pp. 131-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-4/