In this article we study the fractional $p$-Laplacian Kirchhoff type problem in \(\mathbb{R}^N\), $$ \Big(a+b\int\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}\,dx\,dy\Big) (-\Delta)_p^s u+\lambda V(x)|u|^{p-2}u=f(x,u)+g(x,u), $$ where \(s\in(0,1)\), \(2\leq p<\infty\), \(N >sp\), \(a, b, \lambda >0\) are parameters. Under suitable assumptions on \(V, f\) and \(g\), if \(b\) is sufficiently small and \(\lambda\) is large enough, we show that the existence of at least two different nontrivial solutions by combining the variational methods and the truncation technique. At the same time, we explore the asymptotic behavior of solutions as \(b\to 0\) and \(\lambda\to \infty\). We also obtain the nonexistence of nontrivial solutions when \(a\) is large enough. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/15/abstr.html

This work is devoted to the analysis of fuzzy fractional delay differential equations (FDDEs) governed by the generalized Caputo fractional derivative (GCFD). By combining stepwise approximation methods with suitable Gronwall-type inequalities, we establish the existence and uniqueness of solutions. Furthermore, we derive explicit criteria that guarantee the finite-time stability. The theoretical contributions are illustrated with numerical simulations, confirm the analytical findings and demonstrate the effectiveness of the proposed framework in capturing the dynamical behavior of fuzzy fractional delay models. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/07/abstr.html

In this article, using the De Giorgi-Nash-Moser method, we obtain an interior Holder continuity of weak solutions to nonlocal \(p\)-Laplacian type Schrodinger equations given by an integro-differential operator \(L^p_K\) (\(p >1\)), $$\displaylines{ L^p_K u+V|u|^{p-2} u=0 \quad\text{in } \Omega, \cr u=g \quad \text{in } \mathbb{R}^n\backslash \Omega. }$$ Where \(V=V_+-V_-\) with \((V_-,V_+)\in L^1_{loc}(\mathbb{R}^n)\times L^q_{loc}(\mathbb{R}^n)\) for \(q >\frac{n}{ps} >1\) and \(0< s< 1\) is a potential such that \((V_-,V_+^{b,i})\) belongs to the \((A_1,A_1)\)-Muckenhoupt class and \(V_+^{b,i}\) is in the \(A_1\)-Muckenhoupt class for all \(i\in\mathbb{}N\). Here, \(V_+^{b,i}:=V_+\max\{b,1/i\}/b\) for an almost everywhere positive bounded function \(b\) on \(\mathbb{R}^n\) with \(V_+/b\in L^q_{ loc}(\mathbb{R}^n)\), \(g\in W^{s,p}(\mathbb{R}^n)\) and \(\Omega\subset\mathbb{R}^n\) is a bounded domain with Lipschitz boundary. In addition, we prove local boundedness of weak subsolutions of the nonlocal \(p\)-Laplacian type Schrodinger equations. Also we obtain the logarithmic estimate of the weak supersolutions which play a crucial role in proving Holder regularity of the weak solutions. We note that all the above results also work for a nonnegative potential in \(L^q_{loc}(\mathbb{R}^n)\) (\(q >\frac{n}{ps} >1\), \(0< s< 1\)). For more information see https://ejde.math.txstate.edu/Volumes/2025/83/abstr.html

In this article, we study the boundedness of operators of Hardy type on generalized central function spaces, such as the generalized central Hardy space \(\mathbf{HA}^{p,r}_\varphi(\mathbb{R}^n)\), the generalized central Morrey space \(\dot{\mathbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\), and the generalized central Campanato space \(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\), with \(p\in(1,\infty)\), and \(\varphi(t):(0,\infty)\to (0,\infty)\). We first show that \(\mathbf{HA}^{p',r'}_\varphi (\mathbb{R}^n)\) is the predual of \(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\). After that, we investigate the boundedness of operators of Hardy type on those spaces. By duality, we obtain the boundedness characterization of function \(b\in \dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\) via the \(\dot{\textbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\)-boundedness of commutator \([b,\mathcal{H}^*]\). For more information see https://ejde.math.txstate.edu/Volumes/2025/82/abstr.html

This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t>0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t>0,\cr w_t=\Delta w+\gamma u-\delta w, \quad x \in \Omega,\; t>0 }$$ with homogeneous Neumann boundary conditions, where \(\Omega \subset \mathbb{R}^n\) \((n \in \{2,3\})\) is an open ball, \(m, p \in \mathbb{R}\), \(\chi, \xi, \alpha, \beta, \gamma, \delta >0\) are constants. The main result asserts finite-time blow-up of solutions to this system with some positive initial data when \(\chi\alpha-\xi\gamma >0\), \(p \ge 2\) and \(p-m>2/n\). For more information see https://ejde.math.txstate.edu/Volumes/2025/81/abstr.html

In this article, we study the existence of non-radial positive solutions of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+u+V(|x|)\Phi(x)u =Q(|x|) |u|^{p-1}u, \quad x\in \mathbb{R}^3, \cr -\Delta\Phi=V(|x|)u^2,\quad x\in \mathbb{R}^3, }$$ where \(1 < p< 5\) and $V, Q$ are radial potential functions. By developing some refined estimates, via the Lyapunov-Schmidt reduction method, we construct infinitely many multi-bump solutions when \(V, Q\) have some suitable algebraical decay at infinity. The maximum points of those multi-bump solutions are located on the top and bottom circles of a cylinder. This result not only gives a new type of multi-bump solutions but also extends the existence of multi-bump solutions to a general class of potential functions with a relatively slow decay rate at infinity. For more information see https://ejde.math.txstate.edu/Volumes/2025/72/abstr.html

We establish new characterization and nonexistence results concerning complete noncompact and stochastically complete m-quasi Yamabe gradient solitons through the applications of a key Bochner type formula jointly with suitable maximum principles dealing, in particular, with the notions of convergence to zero at infinity and polynomial and exponential volume growth. For more information see https://ejde.math.txstate.edu/Volumes/2025/62/abstr.html

This work concerns the inhomogeneous Schr\"odinger equation $$ \mathrm{i}\partial_t u-\mathcal{K}_{s,\lambda}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}. $$ Here, \(s\in\{1,2\}\), \(N>2s\) and \(\lambda>-(N-2)^2/4\). The linear Schr\"odinger operator is \(\mathcal{K}_{s,\lambda}:= (-\Delta)^s +(2-s)\frac{\lambda}{|x|^2}\), and the focusing source term can be local or non-local $$ F(x,u)\in\{|x|^{-2\tau}|u|^{2(q-1)}u,|x|^{-\tau}|u|^{p-2} \big(J_\alpha *|\cdot|^{-\tau}|u|^p\big)u\}. $$ The Riesz potential is \(J_\alpha(x)=C_{N,\alpha}|x|^{-(N-\alpha)}\), for certain \(0<\alpha<N\). The singular decaying term \(|x|^{-2\tau}\), for some \(\tau>0\) gives a inhomogeneous non-linearity. One considers the inter-critical regime, namely \(1+\frac{2(s-\tau)}N<q<1+\frac{2(s-\tau)}{N-2s}\) and \(1+\frac{2(s-\tau)+\alpha}{N}<p<1+\frac{2(s-\tau)+\alpha}{N-2s}\). The purpose is to prove the finite time blow-up of solutions with datum in the energy space, not necessarily radial or with finite variance. The assumption on the data is expressed in two different ways. The first one is in the spirit of the potential well method due to Payne-Sattinger. The second one is the ground state threshold standard condition. The proof is based on Morawetz estimates and a non-global ordinary differential inequality. This work complements the recent paper by Bai and Li [4] in many directions. For more information see https://ejde.math.txstate.edu/Volumes/2025/55/abstr.html

In this article, we establish bilinear estimates for the nonlinear term appearing in fluid mechanics models posed in bounded domains of 2D and 3D. Also, we give an example to apply the estimates in a 2D bounded domain. For more information see https://ejde.math.txstate.edu/conf-proc/26/c2/abstr.html

The Cauchy problem for the nonlinear Schrodinger equation is called unconditionally well posed in a data space \(E\) if it is well posed in the usual sense and the solution is unique in the space \(C([0,T]; E)\). In this paper, this notion of the unconditional well-posedness is redefined so that it covers \(L^p\)-based Sobolev spaces as data space \(E\) and it is equivalent to the usual one when \(E\) is an \(L^2\)-based Sobolev space \(H^s\) Based on this definition, it is shown that the Cauchy problem for the 1D cubic NLS is unconditionally well posed in Bessel potential spaces \(H^s_p\) for \(4/3<p\le 2\) under certain assumptions on \(s\). For more information see https://ejde.math.txstate.edu/Volumes/2025/41/abstr.html