In the present paper, we study a class of quasilinear Choquard equations involving N -Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.
In this paper, we study global multiplicity result for a class of modified quasilinear singular equations involving the critical exponential growth:where Ω is a smooth bounded domain in R 2 , 0 < q < 3 and α : Ω → (0, +∞) such that α ∈ L ∞ (Ω).The function f : Ω × R → R is continuous and enjoys critical exponential growth of Trudinger-Moser type. Using a sub-super solution method, we show that there exists some Λ * > 0 such that for all λ ∈ (0, Λ * ) the problem has at least two positive solutions, for λ = Λ * , the problem achieves at least one positive solution and for λ > Λ * , the problem has no solution.
In this article, we investigate the existence of the positive solutions to the following class of quasilinear Schrödinger equations involving Stein-Weiss type convolutionis a continuous function with critical exponential growth in the sense of the Trudinger-Moser inequality and F (x, s) = s 0 f (x, t)dt is the primitive of f .
In this article, we consider the following modified quasilinear critical Kirchhoff-Schrödinger problem involving Stein-Weiss type nonlinearity:is the critical exponent with respect to the doubly weighted Hardy-Littlewood-Sobolev inequality (also called Stein-Weiss type inequality). Then by establishing a concentration-compactness argument for our problem, we show the existence of infinitely many nontrivial solutions to the equations with respect to the parameter λ by using Krasnoselskii's genus theory, symmetric mountain pass theorem and Z 2 -symmetric version of mountain pass theorem for different range of q. We further show that these solutions belong to L ∞ (R N ).
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