Articles written in Proceedings – Mathematical Sciences

• Composition of variable co-efficient singular integral operators

In this paper we give a formula for composition of two singular integral operators with variable co-efficients by explicitly calculating the lower order terms. Also we discuss the boundedness of the lower order terms inLp-spaces.

• Positive solutions of the semilinear Dirichlet problem with critical growth in the unit disc in ℝ2

We prove the existence of a positive solution of the following problem −Δu=f(r,u) inDu&gt;0u=0, on ∂D whereD is the unit disc in ℝ2 andf is a superlinear function with critical growth.

• Critical sobolev exponent problem in ℝn(n ≥ 4) with neumann boundary condition

In this paper we study the existence and non existence of positive solution for the critical Sobolev exponent problem − Δu =u(n + 2)/(n − 2) +λα(x)u) in Ω$$\frac{{\partial u}}{{\partial v}} = 0 on \partial B$$, where Ω is a bounded domain in ℝn(n ≥ 4).

• Non-existence of nodal solution form-Laplace equation involving critical Sobolev exponents

In this paper we study the non-existence of nodal solutions for critical Sobolev exponent problem-div(|∇u|m−2u)=|u|p-1u+|u|q-1u inB(R)u = 0 on ∂B(R) whereB(R) is a ball of radiusR in ℝn.

• Formula for a solution ofut +H(u,Du) =g

We study the continuous as well as the discontinuous solutions of Hamilton-Jacobi equationut +H(u,Du) =g in ℝn x ℝ+ withu(x, 0) =u0(x). The HamiltonianH(s,p) is assumed to be convex and positively homogeneous of degree one inp for eachs in ℝ. IfH is non increasing ins, in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019