We study the problem of the existence and nonexistence of positive solutions to a superlinear second–order divergence type elliptic equation with measurable coefficients −∇ · a · ∇u = u (∗), p > 1, in an unbounded cone–like domain G ⊂ R (N ≥ 3). We prove that the critical exponent p∗(a,G) = inf{p > 1 : (∗) has a positive supersolution at infinity in G } for a nontrivial cone– like domain is alw...

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 ...

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...

‎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 ...

We study integrability conditions for existence and nonexistence of a local-in-time integral solution fractional semilinear heat equations with rather general growing nonlinearities in uniformly local $$L^p$$ spaces. Our main results about this matter consist Theorems 1.4, 1.6, 5.1 5.3. introduce supersolution an equation which can be applied to nonlocal parabolic equation. When the nonlinear t...