In this note we establish multiple solutions for a semilinear elliptic equation with superlinear nonlinearility without assuming any symmetry.

We study the large time behavior of solutions for the semilinear parabolic equation ∆u+V up−ut = 0. Under a general and natural condition on V = V (x) and the initial value u0, we show that global positive solutions of the parabolic equation converge pointwise to positive solutions of the corresponding elliptic equation. As a corollary of this, we recapture the global existence results on semil...

In this article, we show the existence and uniqueness of smooth solutions for boundary-value problems of semilinear elliptic systems.

We consider an inverse problem regarding the detection of small conductivity inhomogeneities in a boundary value for semilinear elliptic equation. For such problem, that is related to cardiac electrophysiology, asymptotic expansion potential due presence was established [4]. Starting from this we derive Lipschitz continuous ...

Let L be a bounded linear Fredholm mapping of index zero, mapping a Banach space X into a Banach space 7. Then necessary and sufficient conditions for the solvability of the operator equation Lu = ƒ for ƒ e Y are well known. However the same satisfactory state of affairs does not hold for semilinear operator equations in which a compact nonlinear operator Nu is added to the right hand side of L...

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...

Abstract. Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discret...