相关论文: Global bifurcation diagrams of positive solutions …
In this paper we find out some new blow-up estimates for the positive explosive solutions of a paradigmatic class of elliptic boundary value problems of superlinear indefinite type. These estimates are obtained by combining the scaling…
The paper is concerned with positive solutions to problems of the type \begin{equation*} -\Delta_{\mathbb{B}^N} u - \lambda u = a(x) |u|^{p-1}\;u \, + \, f \, \;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})},…
We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic…
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…
The paper studies families of positive solution curves for non-autonomous two-point problems \[ u"+\lambda f(u)-\mu g(x)=0, \;\; -1<x<1, \;\; u(-1)=u(1)=0 \] depending on two positive parameters $\lambda$ and $\mu$. We regard $\lambda$ as a…
In this work we study the nonnegative solutions of the elliptic system \Delta u=|x|^{a}v^{\delta}, \Delta v=|x|^{b}u^{\mu} in the superlinear case \mu \delta>1, which blow up near the boundary of a domain of R^{N}, or at one isolated point.…
We study the one-dimensional nonlocal elliptic equation \begin{eqnarray*} -\left(\int_0^1 \vert u(x)\vert^p dx + b\right)^q u''(x) &=& \lambda u(x)^p, \quad x \in I:= (0,1), \ u(x) > 0, \ x\in I, \\ u(0) &=& u(1) = 0, \end{eqnarray*} where…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing,…
We are concerned with the nodal set of solutions to equations of the form \begin{equation*} -\Delta u = \lambda_+ \left(u^+\right)^{q-1} - \lambda_- \left(u^-\right)^{q-1} \quad \text{in $B_1$} \end{equation*} where $\lambda_+,\lambda_- >…
We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…
In this paper, we ascertain the global $\lambda$-structure of the set of positive and negative solutions bifurcating from $u=0$ for the semilinear elliptic BVP \begin{equation*} \left\{\begin{array}{ll} -d\Delta u= \lambda\langle…
In this paper, we study the positivity and (uniform) exponential stability of a large class of perturbed semigroups. Our approach is essentially based on the feedback theory of infinite-dimensional linear systems. The obtained results are…
In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…
It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…
In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has…
We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic…
We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form $$ \left\{ \begin{aligned} \Delta_{p} u&=v^{m}|\nabla u|^{\alpha}&&\quad\mbox{ in }\Omega,\\ \Delta_{p} v&=v^{\beta}|\nabla u|^{q}…
We study the nodal set of solutions to equations of the form $$ (-\Delta)^s u = \lambda_+ (u_+)^{q-1} - \lambda_- (u_-)^{q-1}\quad\text{in $B_1$}, $$ where $\lambda_+,\lambda_->0, q \in [1,2)$, and $u_+$ and $u_-$ are respectively the…
In this paper, we prove a global bifurcation result for the existence of non-radial branches of solutions to the paramterized family of $\Gamma$-symmetric problems $-\Delta u=f(\alpha,z,u)$, $u|_{\partial D}=0$ on the unit disc $D:=\{z\in…
In this paper we prove the existence of infinitely many saddle-shaped positive solutions for non-cooperative nonlinear elliptic systems with bistable nonlinearities in the phase-separation regime. As an example, we prove that the system \[…