The Dirichlet problem with sublinear nonlinearities

• Autorzy: Aleksandra Orpel
• Języki publikacji: EN

Abstrakty

EN

We investigate the existence of solutions of the Dirichlet problem for the differential inclusion $0 ∈ Δ x(y) + ∂_{x}G(y,x(y))$ for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional $J(x) = ∫_{Ω}{ 1/2|∇x(y)|² - G(y,x(y))}dy$. 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.

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35J25: Boundary value problems for second-order elliptic equations
• 58E30: Variational principles

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 2
• Strony: 131-140

Daty

wydano

2002

Twórcy

autor

Aleksandra Orpel

• Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/ap78-2-4