Positive solutions of an elliptic equation with strongly nonlinear lower order terms

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Existence of positive solutions of a third order nonlinear differential equation with positive and negative terms

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

Large Solutions of Semilinear Elliptic Equations with Nonlinear Gradient Terms

We show that large positive solutions exist for the equation (P±) :∆u±|∇u|q = p(x)uγ in Ω ⊆ RN(N ≥ 3) for appropriate choices of γ > 1,q > 0 in which the domain Ω is either bounded or equal to RN . The nonnegative function p is continuous and may vanish on large parts of Ω. If Ω = RN , then p must satisfy a decay condition as |x| →∞. For (P+), the decay condition is simply ∫∞ 0 tφ(t)dt <∞, wher...

Multiple Solutions for Strongly Resonant Nonlinear Elliptic Problems with Discontinuities

We examine a nonlinear strongly resonant elliptic problem driven by the p-Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the liter...