Existence of very weak solutions to elliptic systems of p-Laplacian type

Existence of Solutions to Indefinite Quasilinear Elliptic Problems of P-q-laplacian Type

We study the indefinite quasilinear elliptic problem −∆u−∆pu = a(x)|u|q−2u− b(x)|u|s−2u in Ω,

EXISTENCE OF WEAK SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN

This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation − ` ∆pu +∆p(u ) ́ + V (x)|u|p−2u = h(u) in RN . Here V is a positive continuous potential bounded away from zero and h(u) is a nonlinear term of subcritical type. Using minimax methods, we show the existence of a nontrivial solution in C loc (R N ) and then show that it decays to zero at infinity wh...

Existence of weak solutions for a class of (p,q)$(p,q)$-Laplacian systems

EXISTENCE OF POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC SYSTEMS INVOLVING THE p-LAPLACIAN

In this article, we study the existence of positive solutions for the quasilinear elliptic system −∆pu = f(x, u, v) x ∈ Ω, −∆pv = g(x, u, v) x ∈ Ω, u = v = 0 x ∈ ∂Ω. Using degree theoretic arguments based on the degree map for operators of type (S)+, under suitable assumptions on the nonlinearities, we prove the existence of positive weak solutions.

Existence of Periodic Solutions of p(t)-Laplacian Systems

In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for p(t)-Laplacian system  d dt (|u̇(t)|p(t)−2u̇(t)) = ∇F (t, u(t)) a.e. t ∈ [0, T ] u(0)− u(T ) = u̇(0)− u̇(T ) = 0, which generalize some existence theorems. 2010 Mathematics Subject Classification: 34C25, 35A15