Positive and maximal positive solutions of singular mixed boundary value problem

Abstract

Abstract:The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities ( ) in differential equations admit a time singularity at = 0 and/or at = T and a strong singularity at = 0. MSC:34B16, 34B18

Existence of solutions for a class of IBVP for nonlinear hyperbolic equations

“…Therefore, mixed problems have attracted much interest and have been studied by many authors. See [1,5,6] and references cited therein. In our case, the Eq.…”

Mixed Initial-Boundary Value Problem for the Capillary Wave Equation

“…Therefore, the mixed problems have attracted much attention and have been studied by many authors. For detailed description of the mixed boundary conditions, see [1][2][3] and the references cited therein. This paper is the first attempt to investigate the inhomogeneous mixed initial-boundary value problem for the dispersive fractional nonlinear equation, considering as an example the famous capillary water wave equation (1).…”

“…For detailed description of the mixed boundary conditions, see [1][2][3] and the references cited therein. This paper is the first attempt to investigate the inhomogeneous mixed initial-boundary value problem for the dispersive fractional nonlinear equation, considering as an example the famous capillary water wave equation (1). Fractional differential equations appear in many applications of the applied sciences, such as the fractional diffusion and wave equations [4], subdiffusion and superdiffusion equations [5], electrical systems [6], viscoelasticity theory [6], control systems [6], bioengineering [7], and finance [8].…”

“…The operator | | 3/2 corresponds to the dispersive relation of the linearized gravity water wave equations for one-dimensional interfaces with surface tension. Furthermore, thanks to the absence of resonances at the quadratic level, one expects the nonlinear dynamics of water waves to be governed by nonlinearity of cubic type like those appearing in (1). Papers [9][10][11] addressed some other applications of fractional Schrödinger equations.…”

On Nonseparated Three‐Point Boundary Value Problems for Linear Functional Differential Equations

“…While the analytic methods are generally used for the investigation of qualitative properties of solutions such as the existence, multiplicity, branching, stability, or dichotomy and generally use techniques of calculus see, e.g., 1-11 and the references in 12 , the functional-analytic ones are based mainly on results of functional analysis and topological degree theory and essentially use various techniques related to operator equations in abstract spaces [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . The numerical methods, under the assumption on the existence of solutions, provide practical numerical algorithms for their approximation 27, 28 .…”