Related papers: A Sub-Supersolution Approach for a Quasilinear Kir…
We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave…
We established a generalized version of the Christ-Kiselev's multi-linear operator technique to deal with the spectral theory of Schr\"odinger operators. As applications, several spectral results of perturbed periodic Schr\"odinger…
A system of two operator equations is considered - one of pseudomonotone type and the other of strongly monotone type - both being strongly coupled. Conditions are given that allow to reduce the solvability of this system to a single…
We devise a lucid and straightforward way for explicitly constructing quasi-periodic wave solutions (also called multi-periodic wave solutions) of supersymmetric equations in superspace $\mathbb{R}_\Lambda^{2,1}$ over two-dimensional…
In this paper we establish the existence of two positive solutions for a class of quasilinear singular elliptic systems. The main tools are sub and supersolution method and Leray-Schauder Topological degree.
In this paper we study the validity of the comparison principle and the sub-supersolution method for Kirchhoff type equations. We show that these principles do not work when the Kirchhoff function is increasing, contradicting some previous…
In this paper we give necessary and sufficient conditions for the existence of solutions to quasilinear equations of Lane--Emden type with measure data on a Carnot group $\mathbb G$ of arbitrary step. The quasilinear part involves operators…
Existence of nodal (i.e., sign changing) solutions and constant sign solutions for quasilinear elliptic equations involving convection-absorption terms are presented. A location principle for nodal solutions is obtained by means of constant…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…
We prove by means of advanced pseudo-monotonicity methods an abstract existence result for parabolic partial differential equations with $\log$-H\"older continuous variable exponent nonlinearity governed by the symmetric part of a gradient…
The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. Our approach combines the sub-supersolutions method and Schauder's fixed point theorem.
In this paper, we study the following semilinear Schr\"odinger system $$ -\triangle u+u=(1+K_\alpha(\epsilon x))|u|^{p-2}u\ in \mathbb{R}^N, u\in H^1(\mathbb{R}^N) $$ where $3\leq p<2^*$ and $\epsilon>0$, $\alpha>0$ are small parameters.…
In the present paper we study the existence of solutions for some nonlocal problems involving Orlicz-Sobolev spaces. The approach is based on sub-supersolutions.
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The…
In this work we establish a local existence theory for the initial value problem associated to the general quasi-linear ultrahyperbolic Schr\"odinger equation.
In the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of…
This paper is concerned with the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u- \Delta(u^2)u =h(u), \ \ \mbox{in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$. Under appropriate assumptions on $V$ and $h$, we…
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…