In this paper, we study the following elliptic problem   ∆u+K(x)u p = 0 in R u > 0 in R (∗) where K(x) is a given function in Cα(R \ 0) for some fixed α ∈ (0, 1), p > 1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (∗) are discussed. ∗Research supported in part by the Natural Science Foundation of China and NSFC †Research supported in part b...

In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at hand, can determine the diffusion, cavity coefficients simultaneously by knowing corresponding localized Dirichlet-Neumann operators.

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...

where u is a real function and ω ∈ R. If one looks for solutions of (1.1) having the form (1.2), the nonlinear Klein-Gordon equation reduces to a semilinear elliptic equation, as well as if one looks for solitary waves of nonlinear Schrödinger equation (see [10], [12] and the papers quoted therein). Many existence results have been established for solutions u of such a semilinear equation, both...

The main purpose of this paper is to establish the existence of nontrivial solutions to semilinear polyharmonic equations with exponential growth at the subcritical or critical level. This growth condition is motivated by the Adams inequality [1] of Moser-Trudinger type. More precisely, we consider the semilinear elliptic equation (−∆) u = f(x, u), subject to the Dirichlet boundary condition u ...

We consider the inverse problem of determining a potential in semilinear elliptic equation from knowledge Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that is uniquely determined by map measured at single boundary point, or integrated against fixed measure. This result valid even when Dirichlet data only given on small subset boundary. also give related uniqueness results Ri...

Abstract The main goal of this paper is to obtain error bounds for parabolic integro-differential equation. derivation these based elliptic and Ritz -Volterra reconstructions introduced by Makridakis Nochetto 2003 then extended - Volterra reconstruction in case integro-parabolic differential problems Reddy Sinha 2015. We proved optimal order certain classes semilinear intergro equations. key po...

In this paper, the authors study an optimal control problem for quasilinear elliptic PDEs with pointwise state constraints. Weak and strong optimality conditions of Pontryagin maximum principle type are derived. In proving these results, we penalized the state constraints and respectively use the Ekeland variational principle and an exact penalization method. In this paper, our aim is to prove ...