In this paper, we consider the existence of positive solutions to the following problem ⎪⎪⎨ ⎪⎪⎩ −div(|∇u|p−2∇u) = ∂F ∂u (u,v)+ ε p−1g(x) in Ω, −div(|∇v|q−2∇v) = ∂F ∂v (u,v)+ εq−1h(x) in Ω, u,v > 0 in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth domain in RN ; F ∈C1((R+)2,R+) is positively homogeneous of degree μ ; g,h ∈C1(Ω)\{0} ; and ε is a positive parameter. Using sub-supersolution method...

We consider an Hamilton-Jacobi equation of the form H(x,Du) = 0 x ∈ Ω ⊂ R , (1) where H(x, p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with ...

In this paper, we study a semilinear p -Laplacian problem −Δpu+h(x)|∇u| = b(x)g(u), u > 0, x ∈ R , lim |x|→∞ = 0, where q ∈ (p− 1, p], b, h ∈Cα loc(R) for some α ∈ (0,1), h(x) 0, b(x) > 0,∀x ∈ RN , and g ∈ C1((0,∞),(0,∞)) which may be singular at 0 . Using a sub-supersolution argument and a perturbed argument, we obtain the existence of entire solutions to the problem. No monotonicity condition...

A [Formula: see text]-Laplacian elliptic problem in the presence of both strongly singular and text]-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques sub-supersolution method to establish existence an unbounded branch positive solutions, which bounded text]-direction bifurcates from infinity at text]. As consequence result, we determine intervals ...

Abstract In this paper, the existence of a solution for an anisotropic variable exponent system is obtained and proved under general hypotheses. By considering additional conditions, it multiplicity result. The proofs are based on application appropriated $L^{\infty }$ L ∞ </mml:ma...

‎In this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-Laplacian oprator and singular nonlinearities‎. ‎We‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ We find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎We use the method ...

In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations systems, exhibiting both singular convective reaction terms. The importance boundary conditions (Dirichlet, Neumann, or Robin) is also discussed. Existence achieved via sub-supersolution truncation techniques, fixed point theory, nonlinear regularit...