On the logistic equation for the fractional p-Laplacian

We consider a Dirichlet problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic-type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.     

Existence and Asymptotic Behavior of Boundary Blow-up Weak Solutions for Problems Involving the p-Laplacian

Let D⊂R^N(N ≥ 3), be a smooth bounded domain with smooth boundary ∂D. In this paper, the existence of boundary blow-upweak solutions for the quasilinear elliptic equation Δ_pu=λk(x) f (u) in D(λ > 0 and 1 < p < N), is obtained under new conditions on k. We give also asymptotic behavior near the boundary of such solutions.     

带不定权非线性边界的p-Laplacian问题解的存在性

研究了一类带不定权非线性边界的p-Laplacian椭圆方程.获得了当非线性边界的特征值参数小于第二特征值时,该方程存在非平凡解.主要工具为环绕定理.     

Eigenproblem for p-Laplacian and nonlinear elliptic equation with nonlinear boundary conditions

In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalue problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov–Robin.     

无界区域上含p-Laplacian的共振问题

本文利用变分方法研究如下边值问题的可解性:-△pu=μQ（x）|u|p-2u+f（x,u）,u∈D_0~1,p（Ω）,其中Ω是RN中的开集,1相似文献   

含非对称临界非线性项的p-Laplace方程的多解问题

本文考虑含非奇对称临界非线性项的p-Laplace方程Dirichlet问题。运用改进的集中列紧原理证明了在某些指数条件下非奇对称的临界非线性项仍能保证无穷多弱解的存在性。     

一维p-Laplacian的加权特征值的最佳估计

In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.     

Evolution p-Laplacian equations with nonlinear source and measure data

In this article we study the existence of solutions for the evolution p-Laplacian equation with strongly nonlinear sources for initial values prescribed as measures.     

测度链上p-Laplacian 边值问题的三个正对称解

该文研究了p-Laplacian 动力边值问题 (g(u^△(t)))^▽+a(t)f(t, u(t))=0, t ∈ [0, T] _T, u(0)=u(T)=w, u^△(0)=-u^△(T) 正解的存在性. 其中w是非负实数, g(ν)=|ν| ^p-2ν, p>1 . 根据对称技巧和五泛函不动点定理, 证明了边值问题至少有三个正的对称解, 同时, 给出了一个例子验证了我们的结果.     

Resonance for p-Laplacian and asymmetric nonlinearities

In the present paper, we aim to investigate the existence of solutions for the quasilinear boundary value problem involving fractional operators in the ψ-fractional space H([0, T],R) with asymmetric nonlinearities.     

p-Laplacian方程的Aubry-Mather集

本文通过引进合适的作用-角变量变换并结合新的估计方法,对p-Laplacian方程的Poincare映射应用推广的Aubry-Mather定理,证明了一类p-Laplacian方程的Aubry-Mather集的存在性.     

含极限次临界增长项p-Laplace方程的无穷多解

讨论了有界光滑区域上一类p-Laplace方程,非线性项具奇对称性且在无穷远为极限次临界增长．证明了变分泛函在大范围内满足推广的Palais-Smale条件,构造了变分泛函的一列临界值,进而得到了无穷多个弱解的存在性,对应泛函的能量趋于正无穷．所得到的结果推广了次临界增长的情形．     

Existence of solutions for discrete p-Laplacian with potential boundary conditions

We are concerned with the existence of solutions for some discrete p-Laplacian equations subjected to a potential type boundary condition. Our approach is a variational one and relies on Szulkin's critical point theory. We obtain the existence of solutions in a coercive case as well as the existence of non-trivial solutions when the corresponding energy functional has a ‘mountain pass’ geometry.     

Uniqueness for an overdetermined boundary value problem for the p-Laplacian

For set , and let be a measure with compact support. Suppose, for , there are functions and (bounded) domains , both containing the support of with the property that in (weakly) and in the complement of . If in addition is convex, then and .

     

A Note on the p-Laplacian Equation with Singular Coefficients

We consider the solvability of the Dirichlet problem in a unit n-ball for the p-Laplacian equation with singular coefficients which are singular not only as |x| tends to 1 but also as |x| tends to 0. The existence and regularity of positive radial solutions are proved under some conditions related to parameters p, r, λ and q.     

一维p-拉普拉斯三个正解的存在性

考虑边值问题:(p(x'(t)))'+q(t)f(t,x(t),x'(t))=0,P>1,t∈[0,1],边值条件为x(0)=x(1)=0或x(0)=x'(1)=0．借助于一个新的不动点定理我们获得了存在至少三个正解的充分条件．问题的关键是非线性项f依赖于未知函数的一阶导数．最后,给出一个具体的例子．     

Riemann流形上改进的p-Laplace方程的梯度估计

本文研究Riemann流形上的改进的p-Laplace方程,运用截断函数的估计、Hessian比较定理和Laplace比较定理,得到该方程正解的梯度估计.并应用该结论,得到在Riemann流形上关于改进的p-Laplace方程正解的Harnack不等式和Liouville型定理.     

Oscillation and nonoscillation of perturbed nonlinear equations with p-Laplacian

In this paper, we analyze oscillatory properties of perturbed half-linear differential equations (i.e., equations with one-dimensional p-Laplacian). The presented research covers the Euler and Riemann–Weber type equations with very general coefficients. We prove an oscillatory result and a nonoscillatory one, which show that the studied equations are conditionally oscillatory (i.e., there exists a certain threshold value that separates oscillatory and nonoscillatory equations). The obtained criteria are easy to use. Since the number of perturbations is arbitrary, we solve the oscillation behavior of the equations in the critical setting when the coefficients give exactly the threshold value. The results are new for linear equations as well.     

一维奇异p-Laplacian方程多解的存在性

该文通过利用Leggett-Williams定理,建立了一维奇异p-Laplacian非线性边值问题(\varphi(u'))'+a(t)f(u)=0,\u'(0)=u(1)=0 (或者u(0)=u'(1)=0),其中\varphi(s)=|s|^{p-2}s, p>1三解的存在性定理,推广并丰富了以往文献的一些结论.