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In this paper, we deal with the blow-up and global solutions of the following p-Laplacian parabolic problems with Neumann boundary conditions:
In this paper, the time and norm optimal control problems of controlled heat equations with a weight function are considered. For the time optimal problems, we study the following two cases: one is for equatio...
Considering the effect of variable viscosity and the phenomenon of flow separation, the MHD Cu/Ag-Water nanofluids through a permeable wedge are investigated. The governing equations of flow and energy are red...
By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We...
Using some recent results of the Riesz decomposition method for sharp estimates of certain boundary value problems of harmonic functions in (St. Cer. Mat. 27:323-328, 1975), the boundary behaviors of upper and lo...
The present paper deals with the dependence of eigenvalues of 2nth order boundary value transmission problems on the problem. The eigenvalues depend not only continuously but also smoothly on the problem. Some ne...
We obtain infinitely many nontrivial periodic solutions for a class of damped vibration problems, where nonlinearities are superlinear at infinity and primitive functions of nonlinearities are allowed to be si...
The stability and convergence of a linearly extrapolated second order backward difference (BDF2-LE) time-stepping scheme for solving viscoelastic fluid flow in
...
In this paper, we consider a free boundary problem describing the invasion of a generalist predator into a prey population. We analytically derive the conditions guaranteeing the existence and uniqueness of th...
In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Morse theory and the Ljusternik...
This learning pacts with the MHD mixed convection flow of Casson fluid over a stretching surface. Examination is achieved in presence of Hall and thermal radiation effects. Heat and mass transfer analysis is d...
This paper is concerned with the long-time behavior for a class of N-dimensional thermoelastic coupled structure equations with structural damping and past history thermal memory
In this paper, we are concerned with the multiplicity of solutions for a Schrödinger problem. A weaker super-quadratic assumption is required for the nonlinearity. Then we give a new proof for the infinite sol...
In this article, we devote ourselves to building a stabilized finite volume element (SFVE) method with a non-dimensional real together with two Gaussian quadratures of the nonlinear incompressible viscoelastic...
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume...
In this paper, we consider the existence of multiple positive solutions for Kirchhoff-Schrödinger-Poisson system with the nonlinear term containing both general singularity and quasicritical nonlinearity. By c...
A regular 2mth-order spectral problem with self-adjoint boundary conditions is considered in this paper. The continuous dependence of eigenvalues and normalized eigenfunctions on the problem is researched. The de...
Spatiotemporal patterns driven by cross-diffusion of a uni-directional consumer-resource (C-R) system with Holling-II type functional response are investigated in this paper. The existence of a unique positive...
We consider a Keller-Segel-Euler model and prove a regularity criterion of the local strong solutions in a 3D bounded domain Ω.
In this paper, we apply critical point theory and variational methods to study the multiple solutions of boundary value problems for an impulsive fractional differential equation with p-Laplacian. Some new cri...
In this paper, we prove the existence of global weak solutions for a model described by the fractional Heisenberg equation for the magnetization field and the viscoelastic integro-differential equation for the...
Based on an equivalent integral equation of a new type for a class of fractional evolution equations, which is different from those obtained in the existing literature, the paper investigates a class of fracti...
This paper proves the global well-posedness for the 2D Cahn-Hilliard-Boussinesq and a related system with partial viscous terms on bounded domains.
This paper focuses on the maximum and minimum solutions for a fractional order differential system, involving a p-Laplacian operator and nonlocal boundary conditions, which arises from many complex processes such...
We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit ...
We have investigated an initial-boundary problem for the perturbation equations of rotating, incompressible, and viscous magnetohydrodynamic (MHD) fluids with zero resistivity in a horizontally periodic domain...
The initial boundary value problem of a class of Kirchhoff equations with strong damping and nonlinear dissipation is considered. By modifying Vitillaro’s argument, we prove a blow-up result for solutions with...
In this manuscript, we investigate some appropriate conditions which ensure the existence of at least one solution to a class of fractional order differential equations (FDEs) provided by
The main objective of this paper is to investigate the dynamic bifurcation for the granulation convection in the solar photosphere. Based on the dynamic bifurcation theory, which is established by Ma and Wang ...
This paper is mainly devoted to studying one kind of the second order differential equation. Under periodic-integrable boundary value condition, the existence of the solutions of this equation is discussed by ...
In this paper we study the existence of sign-changing solutions for nonlinear problems involving the fractional Laplacian
The Riemann problem for a one-dimensional nonlinear wave system with different gamma laws is considered. By the properties of wave curves, we observe that this system does not contain the composite wave compar...
We study the existence of solutions to a nonlinear fractional differential equation in Hilbert spaces associated with three-point boundary conditions at resonance
...In this paper we derive the Pohozaev-type inequalities for p-Laplacian equations and weighted quasi-linear equations and then prove some non-existence results for the positive solutions of these equations in a...
We study the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations subject to multi-point boundary conditions which contain fractional d...
The original article was published in Boundary Value Problems 2015 2015:18
The original article was published in Boundary Value Problems 2012 2012:40
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