Solutions For Singular p-Laplacian Equations Research Articles

Sufficient and Necessary Conditions on the Existence and Estimates of Boundary Blow-Up Solutions for Singular p-Laplacian Equations

Sufficient and Necessary Conditions on the Existence and Estimates of Boundary Blow-Up Solutions for Singular p-Laplacian Equations

Solutions for singular p-Laplacian equation in R n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆pu = f(x)u−α + λg(x)uβ in RN; where N ≥ 3, 1 0, 0 Λ.

Ground state solutions for singular p-Laplacian equation in [formula omitted

In this work, we study the ground state solution for the class of singular quasilinear elliptic problem of the form − div ( | x | − a p | ∇ u | p − 2 ∇ u ) + h ( | x | ) | u | m − 2 u = H ( | x | ) | u | q − 2 u , x ∈ R N , where 1 < p < N , a < N − p p and h ( r ) , H ( r ) ⩾ 0 . We prove the compactly embedding results of the weighted Z = D a , r 1 , p ( R N ) ∩ L h , r m ( R N ) space of radially symmetric functions and then obtain the existence of nontrivial ground state solution.

Positive solutions for singular p-Laplacian equations with sign changing nonlinearities using inequality theory

In this paper, general existence theorems are presented for the singular equation - ( ϕ p ( u ′ ) ) ′ = q ( t ) f ( u ) + r ( t ) g ( u ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = 0 . Throughout, our nonlinearity is allowed to change sign. The singularity may occur at u = 0.