Semilinear problems on the half space with a hole

Plane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

On the Existence of a Positive Solution for a Semilinear Elliptic Equation in the Upper Half Space

The existence result of a fuzzy implicit integro-differential equation in semilinear Banach space

In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎ ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then...

HALF-EIGENVALUES OF SELF-ADJOINT, 2mTH ORDER DIFFERENTIAL OPERATORS AND SEMILINEAR PROBLEMS WITH JUMPING NONLINEARITIES

We consider semilinear boundary value problems of the form Lu(x) = f(x, u(x)) + h(x), x ∈ (0, π), (1) where L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, π], together with appropriate boundary conditions at 0 and π, while f : [0, π] × R → R is a Carathéodory function and h ∈ L2(0, π). We assume that the limits a(x) := lim ξ→∞ f(x, ξ)/ξ, b(x) := lim ξ→−∞ f(x...

Resonant semilinear problems with nonlinear term depending on the derivative ✩

We study the existence of solution for a boundary value problem at resonance where the nonlinearity depends only on the derivative. In a sense, we can say that the problem considered is strongly resonant. Our proofs make use of the Lyapunov–Schmidt reduction; in so doing, we are led with the asymptotic estimate of the corresponding bifurcation equation.  2004 Elsevier Inc. All rights reserved.