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Displaying 521 – 540 of 1900

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Existence and uniqueness results for solutions of nonlinear equations with right hand side in L 1

A. Fiorenza, C. Sbordone (1998)

Studia Mathematica

We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here f ∈ L 1 ( Ω ) and the solution belongs to the so-called grand Sobolev space W 0 1 , 2 ) ( Ω ) . This is the proper space when the right hand side is assumed to be only L 1 -integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.

Existence of a renormalized solution of nonlinear degenerate elliptic problems

Youssef Akdim, Chakir Allalou (2014)

Applicationes Mathematicae

We study a general class of nonlinear elliptic problems associated with the differential inclusion β ( u ) - d i v ( a ( x , D u ) + F ( u ) ) ∋ f in Ω where f ∈ L ∞ ( Ω ) . The vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general L ∞ -data.

Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type

Milena Matusik (2012)

Annales Polonici Mathematici

The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.

Existence of extremal periodic solutions for nonlinear evolution inclusions

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2001)

Archivum Mathematicum

We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.

Existence of solution of the nonlinear Dirichlet problem for differential-functional equations of elliptic type

Stanisław Brzychczy (1993)

Annales Polonici Mathematici

Consider a nonlinear differential-functional equation (1) Au + f(x,u(x),u) = 0 where A u : = ∑ i , j = 1 m a i j ( x ) ( ∂ ² u ) / ( ∂ x i ∂ x j ) , x = ( x 1 , . . . , x m ) ∈ G ⊂ ℝ m , G is a bounded domain with C 2 + α (0 < α < 1) boundary, the operator A is strongly uniformly elliptic in G and u is a real L p ( G ̅ ) function. For the equation (1) we consider the Dirichlet problem with the boundary condition (2) u(x) = h(x) for x∈ ∂G. We use Chaplygin’s method [5] to prove that problem (1), (2) has at least one regular solution in a suitable class of functions. Using the method of upper and lower...

Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (1999)

Annales Polonici Mathematici

We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.

Currently displaying 521 – 540 of 1900