Communications on Pure and Applied Analysis: latest papers Latest articles for selected journal Singular periodic solutions for the $p$-Laplacian in a punctured domain p_c$ can singular periodic solutions exist; while if $1 < p \le p_c$ then all of the solutions have no singularity. By the singular exponent $q_s=p-1$, we mean that in the case when $q=q_s$, completely different from the remaining case $q\ne q_s$, the problem may or may not have solutions depending on the coefficients of the equation. ]]> Shanming Ji, Yutian Li, Rui Huang and Jingxue Yin Wed, 1 Mar 2017 08:00:00 GMT Long-term stability for KdV solitons in weighted $H^s$ spaces Brian Pigott and Sarah Raynor Wed, 1 Mar 2017 08:00:00 GMT Center conditions for generalized polynomial Kukles systems Jaume Giné Wed, 1 Mar 2017 08:00:00 GMT Diffusive predator-prey models with stage structure on prey and Beddington-DeAngelis functional responses Seong Lee and Inkyung Ahn Wed, 1 Mar 2017 08:00:00 GMT Existence and upper semicontinuity of $(L^2,L^q)$ pullback attractors for a stochastic $p$-Laplacian equation Linfang Liu and Xianlong Fu Wed, 1 Mar 2017 08:00:00 GMT Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting Laplacian Feng Du and Adriano Cavalcante Bezerra Wed, 1 Mar 2017 08:00:00 GMT Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity monotonicity of $f(s)/s$ and the so-called Ambrosetti-Rabinowitz condition are not required. ]]> Minbo Yang, Jianjun Zhang and Yimin Zhang Wed, 1 Mar 2017 08:00:00 GMT Liouville theorems for elliptic problems in variable exponent spaces Sylwia Dudek and Iwona Skrzypczak Wed, 1 Mar 2017 08:00:00 GMT Asymptotic behavior of solutions to a nonlinear plate equation with memory Yongqin Liu Wed, 1 Mar 2017 08:00:00 GMT Global dynamics of solutions with group invariance for the nonlinear Schrödinger equation Takahisa Inui Wed, 1 Mar 2017 08:00:00 GMT Existence and stability of periodic solutions for relativistic singular equations Jifeng Chu, Zaitao Liang, Fangfang Liao and Shiping Lu Wed, 1 Mar 2017 08:00:00 GMT The existence and nonexistence results of ground state nodal solutions for a Kirchhoff type problem 0$, $\lambda < a\lambda_1$, $\lambda_1$ is the principal eigenvalue of $(-\triangle, H_0^{1}(\Omega))$. With the help of the Nehari manifold, we obtain that there is $\Lambda > 0$ such that the Kirchhoff type problem possesses at least one ground state nodal solution $u_b$ for all $0 < b < \Lambda$ and $\lambda < a\lambda_1$ and prove that its energy is strictly larger than twice that of ground state solutions. Moreover, we give a convergence property of $u_b$ as $b\searrow 0$. Besides, we firstly establish the nonexistence result of nodal solutions for all $b \geq \Lambda$. This paper can be regarded as the extension and complementary work of W. Shuai (2015)[21], X.H. Tang and B.T. Cheng (2016)[22]. ]]> Xiao-Jing Zhong and Chun-Lei Tang Wed, 1 Mar 2017 08:00:00 GMT Regularity estimates for continuous solutions of $\alpha$-convex balance laws $2n$-convexity. The results are known in the case of the quadratic flux by very different arguments in [14, 10, 8]. We prove that the continuity of $u$ must be in fact $1/2n$-Hölder continuity and that the distributional source term $g$ is determined by the classical derivative of $u$ along any characteristics; part of the proof consists in showing that this classical derivative is well defined at any `Lebesgue point' of $g$ for suitable coverings. These two regularity statements fail in general for $C^{\infty}(R)$, strictly convex fluxes, see [3]. ]]> Laura Caravenna Wed, 1 Mar 2017 08:00:00 GMT S-shaped and broken S-shaped bifurcation curves for a multiparameter diffusive logistic problem with Holling type-III functional response 1,$ $q,r$ are two positive dimensionless parameters, and $\lambda >0$ is a bifurcation parameter. For fixed $p>1,$ assume that $q,r$ satisfy one of the following conditions: (i) $r\leq \eta_{1,p}^{\ast }q$ and $(q,r)$ lies above the curve \begin{eqnarray} \Gamma _1=\{(q,r): q(a)=\frac{a[2a^{p}-(p-2)]}{a^{p}-(p-1)}, \\ \qquad\qquad\qquad r(a)=\frac{a^{p-1}[2a^{p}-(p-2)]}{(a^{p}+1)^2}, \sqrt[p]{p-1} < a < C_{p}^{\ast}\} ; \end{eqnarray} (ii) $r\leq \eta _{2,p}^{\ast }q$ and $(q,r)$ lies on or below the curve $\Gamma _{1},$ where $\eta _{1,p}^{\ast }$ and $\eta _{2,p}^{\ast }$ are two positive constants, and $C_{p}^{\ast }=\left( \frac{p^{2} + 3p - 4 + p\sqrt{p^{2} + 6p - 7}}{4}\right)^{1/p}$. Then on the $(\lambda, \|u\|_{\infty})$ -plane, we give a classification of three qualitatively different bifurcation curves: an S-shaped curve, a broken S-shaped curve, and a monotone increasing curve. Hence we are able to determine the exact multiplicity of positive solutions by the values of $q,$ $r$ and $\lambda $. ]]> Tzung-Shin Yeh Wed, 1 Mar 2017 08:00:00 GMT A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential 0 \quad \text{in} \ \Omega, \quad u = 0 \quad \text{on} \ \partial \Omega, \end{eqnarray} for a totally degenerate potential $K$. Here $\varepsilon >0$ is a small parameter, $\Omega \subset \mathbb{R}^N$ is a bounded domain with a smooth boundary, and $f$ is an appropriate superlinear subcritical function. In particular, $f$ satisfies $0< \liminf_{ t \to 0+} f(t)/t^q \leq \limsup_{ t \to 0+} f(t)/t^q < + \infty$ for some $1< q < + \infty$. We show that the least energy solutions concentrate at the maximal point of the modified distance function $D(x) = \min \{ ( q+1) d(x, \partial A), 2 d(x, \partial \Omega) \}$, where $A = \{ x \in \bar{ \Omega } \mid K(x) = \max_{ y \in \bar{ \Omega } } K(y) \}$ is assumed to be a totally degenerate set satisfying $A^{\circ} \neq \emptyset$. ]]> Shun Kodama Wed, 1 Mar 2017 08:00:00 GMT A sustainability condition for stochastic forest model Tôn Viêt Ta, Linh Thi Hoai Nguyen and Atsushi Yagi Wed, 1 Mar 2017 08:00:00 GMT