CAJ | 학술논문

p-Laplace方程是一类椭圆微分方程，它描述了化学和物理中一类稳定的反映扩散现象。当p＝2时，p-Laplace方程为经典的 Laplace方程，p（t）-Laplace方程可以用来描述“逐点异性”的物理现象，p（t）-Laplace算子比p-Laplace算子有更复杂的非线性性质。方程解的存在性问题是微分方程中讨论较多的问题。利用Banach空间中的理论证明了一类p（t）-Laplace方程在一定条件下解的存在性。
p-Laplace방정시일류타원미분방정，타묘술료화학화물리중일류은정적반영확산현상。당p＝2시，p-Laplace방정위경전적 Laplace방정，p（t）-Laplace방정가이용래묘술“축점이성”적물리현상，p（t）-Laplace산자비p-Laplace산자유경복잡적비선성성질。방정해적존재성문제시미분방정중토론교다적문제。이용Banach공간중적이론증명료일류p（t）-Laplace방정재일정조건하해적존재성。
p-Laplace equation is an elliptic differential equation,which describes the reflection of a class of stable dispersion of chemical and physical phenomena.When p is equal to 2,p-Laplace e-quation is the classical Laplace equation.p(t)-Laplace equation can be used to describe the“phys-ical phenomenon by heterosexual”.p(t)-Laplace operators have more complex nonlinear proper-ties than the p-Laplace operator.The existence of solutions for the problem is discussed frequent-ly in differential equations.This paper proves the existence of solutions in certain conditions of a class of p(t)-Laplace equation by using Banach space theory.