EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR A p-LAPLACE EQUATION WITH POTENTIALS IN R
نویسندگان
چکیده
We study the p-Laplace equation with Potentials − div(|∇u|p−2∇u) + λV (x)|u|p−2u = |u|q−2u, u ∈ W 1,p(RN ), x ∈ RN where 2 ≤ p, p < q < p∗. Using a concentrationcompactness principle from critical point theory, we obtain existence, multiplicity solutions, and concentration of solutions.
منابع مشابه
MULTIPLE SOLUTIONS FOR THE p−LAPLACE OPERATOR WITH CRITICAL GROWTH
In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical con...
متن کاملExistence and Concentration of Positive Solutions for a Quasilinear Elliptic Equation in R
We study the existence and concentration of positive solutions for the quasilinear elliptic equation −ε2u′′ − ε2(u2)′′u + V (x)u = h(u) in R as ε → 0, where the potential V : R → R has a positive infimum and inf∂Ω V > infΩ V for some bounded domain Ω in R, and h is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.
متن کاملSemiconducting properties of passive films formed on AISI 420 stainless steel in nitric acid solutions
This study focuses on the semiconductor properties of passive films formed on AISI 420 stainless steel immersed in four nitric acid solutions under open circuit potential (OCP) conditions. For this purpose, the passivation parameters and semiconductor properties of passive films were derived from potentiodynamic polarization and Mott–Schottky analysis, respectively. The OCP plots showed that th...
متن کاملEXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTION TO A CRITICAL p–LAPLACIAN EQUATION
In this paper, we consider the existence and concentration behavior of positive ground state solution to the following problem { −hΔpu+V (x)|u|p−2u = K(x)|u|q−2u+ |u|p−2u, x ∈ RN , u ∈W 1,p(RN ), u > 0, x ∈ RN , where h is a small positive parameter, 1 < p < N , max{p, p∗ − p p−1} < q < p∗ , p∗ = Np N−p is the critical Sobolev exponent, V (x) and K(x) are positive smooth functions. Under some n...
متن کاملMULTIPLE SOLUTIONS OF A p(x)-LAPLACIAN EQUATION INVOLVING CRITICAL NONLINEARITIES
In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions { −div(|∇u|p(x)−2 ∇u) + |u|p(x)−2 u = f(x, u) in Ω, u = 0 on ∂Ω. We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-co...
متن کامل