Displaying similar documents to “Nonlocal elliptic problems”

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...

On a nonlocal problem for a confined plasma in a Tokamak

Weilin Zou, Fengquan Li, Boqiang Lv (2013)

Applications of Mathematics

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The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms u * ' ( | u > u ( x ) | ) and | u > u ( x ) | , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.