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Dirichlet problems without convexity assumption

Aleksandra Orpel (2005)

Annales Polonici Mathematici

We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem.

Discontinuous elliptic problems in ℝ N without monotonicity assumptions

Silvia Cingolani, Monica Lazzo (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove existence of a positive, radial solution for a semilinear elliptic problem with a discontinuous nonlinearity. We use an approximating argument which requires no monotonicity assumptions on the nonlinearity.

Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)

Colloquium Mathematicae

In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.

Discrete approximations of generalized RBSDE with random terminal time

Katarzyna Jańczak-Borkowska (2012)

Discussiones Mathematicae Probability and Statistics

The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.

Eigenvalue problems with indefinite weight

Andrzej Szulkin, Michel Willem (1999)

Studia Mathematica

We consider the linear eigenvalue problem -Δu = λV(x)u, u ∈ D 0 1 , 2 ( Ω ) , and its nonlinear generalization - Δ p u = λ V ( x ) | u | p - 2 u , u ∈ D 0 1 , p ( Ω ) . The set Ω need not be bounded, in particular, Ω = ℝ N is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues λ n → ∞ .

Currently displaying 121 – 140 of 600