Related papers: Existence of positive solutions for a three-point …
We investigate pointwise upper bounds for nonnegative solutions $u(x,t)$ of the nonlinear initial value problem \begin{equation}\label{0.1} 0\leq(\partial_t-\Delta)^\alpha u\leq u^\lambda \quad\text{ in }\mathbb{R}^n…
In this note we establish existence of solutions of singular boundary value problem $-(p(x)y^{\prime }(x))^{\prime}=q(x)f(x,y,py')$ for $0< x\leq b$ and $y'(0)=0$, $\alpha_{1}y(b)+\beta_{1}p(b)y^{\prime}(b)=\gamma_{1}$ with $p(0)=0$ and…
We consider the nonlinear heat equation $u_t - \Delta u = |u|^\alpha u$ on ${\mathbb R}^N$, where $\alpha >0$ and $N\ge 1$. We prove that in the range $0 < \alpha <\frac {4} {N-2}$, for every $\mu >0$, there exist infinitely many…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
In this paper, we study the initial-boundary value problem of one-dimensional isentropic compressible Euler equations with the source term $\beta\rho|u|^{\alpha}u$. By means of wave decomposition and the uniform a-priori estimates, we prove…
Equation $(-\Delta+k^2)u+f(u)=0$ in $D$, $u\mid_{\partial D}=0$, where $k=\const>0$ and $D\subset\R^3$ is a bounded domain, has a solution if $f:\R\to\R$ is a continuous function in the region $|u|\geq a$, piecewise-continuous in the region…
We analyze the existence of unique solutions of the following class of nonlinear three point singular boundary value problems (SBVPs), \begin{eqnarray*}\label{NL-Singular-P} &&-(x^{\alpha} y'(x))'= x^{\alpha}f(x,y),\quad 0<x<1,\\…
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…
This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\Delta)^2 u=\lambda u+…
We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),…
We study the existence and multiplicity of positive solutions for a family of fractional Kirchhoff equations with critical nonlinearity of the form \begin{equation*}…
We study the non-existence, existence and multiplicity of positive solutions to the following nonlinear Kirchhoff equation:% \begin{equation*} \left\{ \begin{array}{l} -M\left( \int_{\mathbb{R}^{3}}\left\vert \nabla u\right\vert…
In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave-convex nonlinearities: $$({-}{ \Delta})^{\frac{\alpha}{2}}u- \gamma \frac{u}{|x|^{\alpha}}=…
This paper deals with the existence of positive solutions for the nonlinear system q(t)\phi(p(t)u'_{i}(t)))'+f^{i}(t,\textbf{u})=0,\quad 0<t<1,\quad i=1,2,...,n. This system often arises in the study of positive radial solutions of…
The paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the $\phi$-Laplacian equation \begin{equation*} \bigl{(} \phi(u') \bigr{)}' + a(t) g(u) = 0, \end{equation*}…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are…
In this work, we prove the existence of a positive solution to the second-order nonlinear problem $u''+f(t,u,u')=0$ with mixed boundary conditions, where $f$ is an $L^p$-Carath\'eodory function satisfying certain properties. Three boundary…