In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: −∆u+ u = λf(x)|u|q−2u in Ω, ∂u ∂ν = g(x)|u|p−2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.

In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...

We consider a semilinear elliptic equation ∆u+ λf(u) = 0, x ∈ Ω, ∂u

Some oscillation criteria for the second order semilinear elliptic differential equation

We consider a semilinear elliptic system which include the model system of the W−strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in [13]

Some oscillation criteria for the second order semilinear elliptic differential equation

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

Under simple conditions on fi and gi, we show the existence of entire positive radial solutions for the semilinear elliptic system ∆u = p(|x|)f1(v)f2(u) ∆v = q(|x|)g1(v)g2(u), where x ∈ RN , N ≥ 3, and p, q are continuous functions.

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 ...