In this article we focus on inverse problems for a semilinear elliptic equation. We show that potential q in Ln/2+ε, ε>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends results [LLLS21b] where is shown Hölder continuous potentials. Also when map restricted to one point boundary, it possible determine Ln+ε. The authors of [ST22] proved true

In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given. Keywords—Pseudo-hyperbolic partial integro-differential equations; Nonconforming mixed eleme...

In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to the solution o...

We consider the semilinear elliptic problem −Δu + u = λK(x)up + f (x) in Ω, u > 0 in Ω, u ∈ H 0 (Ω), where λ ≥ 0, N ≥ 3, 1 < p < (N + 2)/(N − 2), and Ω is an exterior strip domain in RN . Under some suitable conditions on K(x) and f (x), we show that there exists a positive constant λ∗ such that the above semilinear elliptic problem has at least two solutions if λ∈ (0,λ∗), a unique positive sol...

Let Ω be a C2-bounded domain of Rd, d = 2, 3, and fix Q = (0, T )×Ω with T ∈ (0,+∞]. In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation ∂α t u + Au = fb(u) in Q where 1 < α < 2, ∂α t corresponds to the Caputo fractional derivative of order α, A is an elliptic operator and the nonlinearity fb ∈ C1(R) satisfies fb(0) =...

We prove the existence of a solution to the Monge-Ampère equation detHess(φ) = 1 on a cone over a thrice-punctured two-sphere. The total space of the tangent bundle is thereby a Calabi-Yau manifold with flat special Lagrangian fibers. (Each fiber can be quotiented to three-torus if the the affine monodromy can be shown to lie in SL(3,Z)⋉ R .) Our method is through Baues and Cortés’s result that...

The numerical computation of solitary waves to semilinear elliptic equations in innnite cylinders is investigated. Rather than solving on the innnite cylinder, the equation is approximated by a boundary-value problem on a nite cylinder. Convergence and stability results for this algorithm are given. In addition, it is shown that Galerkin approximations can be used to calculate solitary waves fo...

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0 ≤ u ≤ 1 and ∫ u = m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth Newton method. A regularization of the nonsmooth equation is necessary to obtain the superlinear co...

In this paper, we investigate residual-based a posteriori error estimates for the hp finite element approximation of semilinear Neumann boundary elliptic optimal control problems. By using the hp finite element approximation for both the state and the co-state and the hp discontinuous Galerkin finite element approximation for the control, we derive a posteriori error bounds in L2-H1 norms for t...

This paper deals with second order necessary conditions for optimal solution of optimal control problems governed by semilinear elliptic partial differential equations with pointwise state-control constraints.