Displaying similar documents to “A remark on some nonlinear elliptic problems.”

A symmetrization result for nonlinear elliptic equations.

Vincenzo Ferone, Basilio Messano (2004)

Revista Matemática Complutense

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We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

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

Stanisław Brzychczy (1993)

Annales Polonici Mathematici

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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...