Boundary Blow-up Solutions For P (x)-laplacian Problem

In recent years, the study of the growth conditions of variation problem has attractedmore and more attention for the extremely important practical backgrounds, and theyare mathematical models such as inelastic mechanics, electrorheological fluids, imageprocessing. The boundary blow-up problem which comes from the study on the constantnegative curvature of Riemann surface and the theory of automorphic functions is anemerging research topic. It has important research value in some physical phenomenon. Thispaper studies the existence and asymptotic behavior of blow-up solution of p (x)-Laplacianproblem.This thesis has four chapters.The first chapter introduces the background about the growth conditions of variationproblem and the boundary of blow-up problem.The second chapter investigates the existence and asymptotic behavior of blow-upsolution for a class of special p-Laplacian equation. We prove the result by two kinds ofmethods, one is the simplified Keller-Osserman condition, the other is the upper and lowersolution method.The third chapter studies the existence and asymptotic behavior of blow-up solution forp (x)-Laplacian equation. It mainly concerns the blow-up properties of solutions whenf (u)is elementary function such as exponential function, logarithmic function, powerfunction. When we prove the existence of blow-up solutions, we use the simplifiedKeller-Osserman conditions. For the asymptotic properties, the blow-up rate estimations aregiven.In the fourth chapter, we make a summary and outlook to the contents of thisdissertation.