Existence of solutions to heat equations with singular lower order terms

Existence of Solutions to Singular Elliptic Equations with Convection Terms via the Galerkin Method

In this article, we use the Galerkin method to show the existence of solutions for the following elliptic equation with convection term −∆u = h(x, u) + λg(x,∇u) u(x) > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain, λ ≥ 0 is a parameter, h has sublinear and singular terms, and g is a continuous function.

Existence of Solutions to Nonlocal Elliptic Equations with Discontinuous Terms

In this article, we study the existence of nonnegative solutions for the elliptic partial differential equation −[M(‖u‖p1,p)] ∆pu = f(x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ RN is a bounded smooth domain, f : Ω×R+ → R is a discontinuous nonlinear function.

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

Microlocal Time Decays for Hyperbolic Equations with Lower Order Terms

In this paper we present microlocalised time-decay rates of solutions to hyperbolic equations with constant coefficients with arbitrary lower order terms. A particular attention is paid to regions with multiplicities. AMS Mathematics Subject Classification (2000): 35L30, 35L45

Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations

and Applied Analysis 3 Consequently, the condition u′ 0 0 1.11 is necessary for each solution of 1.7 . Denote usup sup{u t : t ∈ 0,∞ }. 1.12 Definition 1.2. Let u be a solution of 1.7 . If usup < L, then u is called a damped solution. If a solution u of 1.7 satisfies usup L or usup > L, then we call u a bounding homoclinic solution or an escape solution. These three types of solutions have been...