Twoweak solutions for a singular (p,q)-Laplacian problem

Abstract

Here, a singular boundary value problem involving the (p, q)-Laplacian operator in a smooth bounded domain in R N is considered. Using the variational method and critical point theory, the existence of two weak solutions is proved.

The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation

“…Here > 1 is the blow-up time of the weak solutions. At the end of the introduction, we would like to suggest that it is an interesting research problem to study the anisotropic parabolic equation (6) for either ( , )-Laplacian or -biharmonic (see [28][29][30]).…”

On the Oscillation Criteria for Fourth-Order p -Laplacian Differential Equations with Middle Term

“…Since the fourth-order delay differential equations described many real-life applications, such as models related to physical, chemical, and biological phenomena, in the last decades, a lot of research has been done on the oscillatory behavior of fourth-order delay differential equations, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the references cited therein. On the other hand, the p-Laplacian differential equations there are some important applications in continuum mechanics and elasticity theory [15][16][17][18][19][20][21][22][23], the oscillatory behavior of the solutions of fourth-order differential equations with p-Laplacian like operator have been investigated in recent years by using different methods and various techniques, for example, [24][25][26].…”

A Sequence of Radially Symmetric Weak Solutions for Some Nonlocal Elliptic Problem in $${\mathbb {R}}^N$$

“…Laplace equation is the prototype for linear elliptic equations, as the most important partial differential equation of the second order. This equation has a non-linear counterpart, the so-called p-Laplace equation (see [1,13,14,18,19,21,22]). There has been a surge of interest in the p-Laplacian in many different contexts from game theory to mechanics and image processing.…”