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We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings....
In the present paper, the existence of nontrivial solutions of impulsive fractional differential equations with Dirichlet boundary conditions is studied. We apply Morse theory coupled with local linking argume...
In this paper, we approximate the solution of fractional Bagley–Torvik equation by using the exponential spline function and the shifted Grünwald difference operator. The proposed methods reduce to the system ...
A generalized Camassa–Holm equation proposed by Novikov is considered. The existence and uniqueness of a positive weak solution for the equation is established by using a classical method.
The Editors-in-Chief have retracted this article [1] because it shows evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Stockholms Universitet h...
The original article was published in Boundary Value Problems 2014 2014:245
The Editors-in-Chief have retracted this article [1] because it shows evidence of peer review manipulation. In addition, it overlaps significantly with an article by Sun et al. [2] that was simultaneously unde...
The original article was published in Boundary Value Problems 2018 2018:74
The Editors-in-Chief have retracted this article [1] because of overlap with articles from different authors that were simultaneously under consideration with another journal [2, 3]. Additionally, this article...
The original article was published in Boundary Value Problems 2017 2017:67
This paper is concerned with the global existence of solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation. Firstly, based on the Schrödinger approximation techniq...
The Retraction Note to this article has been published in Boundary Value Problems 2021 2021:9
In this paper, we discuss third-order full nonlinear singularly perturbed vector boundary value problems. We first present the existence of solutions for the nonlinear vector boundary value problems without pe...
The present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is su...
This paper is concerned with a class of beam equations with a parameter. By using the fixed point theorems of mixed monotone operator and the properties of cone, we study the non-singular and singular case, re...
In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inher...
This research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the formulation of the model containing snuffing class is pre...
In this paper, several novel existence and multiplicity results are established for a coupled functional differential system with multi-parameters. The discussion is based upon fixed point theory, and our main...
In this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger bou...
By using variational methods, we obtain infinitely many nontrivial periodic solutions for a class of damped vibration systems with superquadratic terms at infinity. By using some weaker conditions, our results...
In this paper, we consider convergence rates to solutions for the damped system of compressible adiabatic flow through porous media with boundary effect. Compared with the results obtained by Pan, the better c...
Any spectral element discretization of the Darcy problem can be efficiently solved by applying the penalty method. This method leads to a system of equations with uncoupled unknowns. We prove a posteriori erro...
This paper is concerned with the existence of extremal mild solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach space E. By employing the method of lower and upper so...
The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of ...
In this paper, we prove the existence of positive ground state solutions of the Schrödinger–Poisson system involving a negative nonlocal term and critical exponent on a bounded domain. The main tools are the m...
In this paper, we develop the theory of differential equations with linear perturbations of second type on time scales. An existence theorem for differential equations with linear perturbations of second type ...
This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures t...
In this paper, we consider the Cauchy problem for the sixth-order multidimensional generalized Boussinesq equation with double damping terms. By using the improved convexity method combined with Fourier transf...
The self-adjoint matrix Sturm–Liouville operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the cons...
In this paper, we consider the solvability, regularity and vanishing viscosity limit of the 3D viscous Boussinesq equations with a Navier-slip boundary condition. We also obtain the rate of convergence of the ...
The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite Sturm–Liouville differential equation with nonloca...
In this paper, we consider the blow-up result of solution for a quasilinear von Karman equation of memory type with nonpositive initial energy as well as positive initial energy. For nonincreasing function
We prove the existence of multiple positive solutions of fractional Laplace problems with critical growth by using the method of monotonic iteration and variational methods.
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