A Fourth Order Singular Elliptic Problem Involving $p$-biharmonic Operator

RETRACTED ARTICLE: Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions

“…where A is the infinitesimal generator of a rotationally invariant Lévy process (see [18]). Now we present a modified maximum principle approach with respect to the Schrödinger operator for the quasilinear Schrödinger equation with a general nonlinear nonlinear optimal control condition (1.1), which plays an important role in our discussions.…”

“…Coveri considered the existence and symmetry of positive solutions for a modified Schrödinger system under the Keller-Osserman type conditions in [17]. Chaharlang and Razania considered the fourthorder singular elliptic problem involving p-biharmonic operator with Dirichlet boundary condition in [18]. The existence of at least one weak solution was proved in two different cases of the nonlinear term at the origin.…”

On the weak solutions of an overdetermined system of nonlinear fractional partial integro-differential equations

“…The standard and typical approach to study the existence of solutions to the nonlinear fractional boundary value problems is the fixed point theory, see for example [1,4,16,35]. But, another well-developed, successful and recently more attracting method is the calculus of variation to investigate the existence of solutions to the differential equation with type of integer order and very recently fractional order, the readers are referred to [7,[11][12][13][17][18][19][20][21]32,33,36] and the references therein to attain more information about this approach.…”

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.…”

“…The parameters in (1.2) have the following meanings: h is the cross-section area, E is the Young modulus, ρ is the mass density, L is the length of the string, and P 0 is the initial tension. In recent years, p-Kirchhoff type problems have been studied by many researchers, (for example see [19,20]). Beside elliptic problems with boundary conditions on bounded domain of R N which have extensive applications in different parts of scient and have been considered by many authors recently, see [21,22], some elliptic problems arise on unbounded domain R N , see [5,38].…”