Existence of positive solutions for some problems with nonlinear diffusion

In this paper we study the existence of positive solutions for problems of the type

where is the -Laplace operator and . If , such problems arise in population dynamics. Making use of different methods (sub- and super-solutions and a variational approach), we treat the cases , and , respectively. Also, some systems of equations are considered.

     

On approximate solutions to some nonlinear diffusion problems

In the paper an approximate solution to a nonlinear diffusion problem in semiconductor production is considered. Some integral operator methods are used to estimate an error between this approximate solution and the exact one.This paper has been written when the author was a Visiting Professor in the Universidad de Extremadura.     

Power series solutions to some nonlinear diffusion problems

In this paper power series solution to some nonlinear diffusion problems in semiconductor production are considered. The convergence proof for power series solutions is presented.This paper has been written when the first author was a Visiting Professor in the Universidad de Extremadura.     

On positive solutions of some nonlinear fourth-order beam equations

The existence, uniqueness and multiplicity of positive solutions of the following boundary value problem is considered:

u⁽⁴⁾(t)−λf(t,u(t))=0, for 0<t<1,u(0)=u(1)=u″(0)=u″(1)=0,

where λ>0 is a constant, f :[0,1]×[0,+∞)→[0,+∞) is continuous.     

Existence of positive solutions of some nonlinear elliptic problems in unbounded domains

In this paper, we study the existence of positive solutions of some nonlinear elliptic problems in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain.     

On strictly positive solutions for some semilinear elliptic problems

Let B be a ball in ${\mathbb{R}^{N}}$ , N ≥ 1, let m be a possibly discontinuous and unbounded function that changes sign in B and let 0 < p < 1. We study existence and nonexistence of strictly positive solutions for semilinear elliptic problems of the form ${-\Delta u=m(x) u^{p}}$ in B, u = 0 on ?B.     

Existence and nonexistence of global positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary

This paper deals with the existence and nonexistence of global positive solutions to in ,

and in . Here is a parameter, is a bounded smooth domain. After pointing out the mistakes in Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary, SIAM J. Math. Anal. 24 (1993), 317-326, by N. Wolanski, which claims that, for the ball of , the positive solution exists globally if and only if , we reconsider the same problem in general bounded domain and obtain that every positive solution exists globally if and only if .

     

On positive solutions for some semilinear periodic parabolic eigenvalue problems

For a bounded domain Ω in , N?2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Lu_λ=λg(x,t,u_λ) in , u_λ=0 on . We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. satisfying some integrability conditions in (x,t) and

     

Multiple positive solutions for nonlinear periodic problems

We consider a nonlinear periodic equation driven by the scalar p-Laplacian and with a Caratheodory asymptotically (p−1)-linear nonlinearity. Using variational methods coupled with suitable truncation techniques, we show that the problem has at least two positive solutions. For the semilinear case (p=2), using Morse theory we show that the problem has three distinct positive solutions.     

The existence of three positive solutions for some nonlinear boundary value problems on the half-line

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line

NontriviaL solutions of some nonlinear elliptic problems

This paper is concerned with a class of semilinear elliptic Dirichlet problems approximating degenerate equations. The aim is to prove the existence of at least 4^k?1 nontrivial solutions when the degeneration set consists of k distinct connected components