Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Abstract

We consider the problem −div(|∇u|In this work, we are interested in studying the existence of solutions to the following quasilinear equation:is not identically zero. We will assume throughout the paper that a(x) ∈ C(R N ). Equations of the above form are mathematical models occuring in studies of the p-Laplace equation, generalized reaction-diffusion theory [1], non-Newtonian fluid theory, and the turbulent flow of a gas in porous medium [2]. In the non-Newtonian fluid theory, the quantity p is characteristic of the medium. Media with p > 2 are called dilatant fluids and those with p < 2 are called pseudoplastics. If p = 2, they are Newtonian fluids. Problem (1) for bounded domains with zero Dirichlet condition has been extensively studied (even for more general sublinear functions). We refer in particular to [3][4][5][6][7][8][9][10] (see also the references therein). When p = 2, the related results have been obtained by [11][12][13][14][15][16] (including bounded domains with zero Dirichlet condition or R N ). Our existence

Nonnegative Solutions of Quasilinear Elliptic Problems With Sublinear Indefinite Nonlinearity

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Remarks on nonexistence of solutions of mixed sublinear and superlinear elliptic equation in RN

“…In [11], Yang obtained that if H ∞ < ∞, the problem (1.18) has a ground state solution for λ ∈ (0, λ 0 ) with some λ 0 > 0.…”