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On the Solvability of an Essentially Nonlinear Elliptic Differential Equation with Nonlocal Boundary Conditions
AbstractSufficient conditions for the existence of a generalized solution to a nonlinear elliptic differential equation with nonlocal boundary...
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Phragmén–Lindelöf theorems for a weakly elliptic equation with a nonlinear dynamical boundary condition
We establish two Phragmén–Lindelöf theorems for a fully nonlinear elliptic equation. We consider a dynamical boundary condition that includes both...
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Explicit Solutions of the Nonlinear Schrödinger-Type Equation
In this work, we focus on the construction of explicit solutions of the nonlinear Schrödinger-type equation, which has various applications in...
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An Inverse Problem for a Quasilinear Elliptic Equation
We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first...
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Jacobian-Elliptic-Function and Rogue-Periodic-Wave Solutions of a Fifth-Order Nonlinear Schrödinger Equation in an Optical Fiber
Optical fiber communication becomes the main research direction in optical networking, computing, telecommunications and data communication. In an...
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Multiple Solutions for an Elliptic Equation from the Antarctic Circumpolar Current
In this paper, a mathematical model of the second order elliptic equation of the Antarctic Circumpolar Current with Dirichlet boundary is...
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Linear and Fully Nonlinear Elliptic Equations with Morrey Drift
We present some results concerning the solvability of linear elliptic equations in bounded domains with the main coefficients almost in VMO, the...
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Worked Out Problem 7: A Nonlinear Elliptic Problem
In this chapter, we consider a scalar nonlinear elliptic PDE as a benchmark for complex material problems in a two-dimensional domain. The aim is to...
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Gradient Estimations for Nonlinear Elliptic Equations on Weighted Riemannian Manifolds
AbstractIn this article, we derive local gradient estimates for positive solutions of a generalized nonlinear weighted elliptic equation
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Nonlinear Elliptic Equations on Weighted Sobolev Space
AbstractThe main objective of this work is to show the existence of solutions for quasilinear elliptic boundary value problem. In addition, we...
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Bifurcation from the essential spectrum for an elliptic equation with general nonlinearities
In this paper, based on some prior estimates, we show that the essential spectrum λ = 0 is a bifurcation point for a superlinear elliptic equation...
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Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds
We establish second order estimates for a general class of fully nonlinear elliptic equations with gradient terms on almost Hermitian manifolds...
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The exact solutions of Fokas-Lenells equation based on Jacobi elliptic function expansion method
The Fokas-Lenells (FL) equation, which is rich in physical property in soliton theory as well as optical fiber, is a generalization of the...
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Nonlinear degenerate elliptic equations with a convection term
We prove some existence and regularity results for the solutions of the Dirichlet problem associated with a nonlinear degenerate elliptic equation...
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New Exact Solitary Wave Solutions of the Perturbed Cubic-Quartic Complex Ginzburg–Landau Equation with Different Nonlinear Refractive Index Structures
In this work, some new exact solitary wave solutions of the perturbed cubic-quartic complex Ginzburg–Landau equation (CQ-CGLE) are obtained. Using a...
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Boundary Lower Estimates for a Class of Fully Nonlinear Elliptic Partial Differential Equations
In this paper we are concerned with the Dirichlet problem for a class of fully nonlinear elliptic partial differential equations. Under structural...
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Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs
The local minimax method (LMM) proposed by Li and Zhou (2001) and Li and Zhou (2002) is an efficient method to solve nonlinear elliptic partial...