Results 21 to 30 of about 15,587,481 (320)
Existence of positive solutions to some nonlinear equations on locally finite graphs [PDF]
, 2016 Let G = (V, E) be a locally finite graph, whose measure μ(x) has positive lower bound, and Δ be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti and Rabinowitz (1973), we establish existence results for some nonlinear ...
A. Grigor’yan, Yong Lin, Y. Yang
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On the existence of positive solutions for generalized fractional boundary value problems
Boundary Value Problems, 2019 The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems.
Arjumand Seemab +3 more
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A Priori Bounds And Existence Of Positive Solutions For Semilinear Elliptic Systems [PDF]
, 2017 We provide a-priori L∞ bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v^p and u^q for any (p,q) lying on the critical Sobolev hyperbola.
Mavinga, Nsoki, Pardo, R.
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Boundary Value Problems, 2018 In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions.
Jianxin He +4 more
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On existence of positive periodic solutions [PDF]
Monatshefte f�r Mathematik, 1998 Let \(\Omega\) be an open convex subset of \(\mathbb{R}^n\). A differential equation \[ \dot x=f(t,x) \tag{1} \] on \(\mathbb{R}\times \text{cl} \Omega\) is considered. It is assumed that the right-hand side of (1) is \(T\)-periodic in \(t\). The main theorem asserts the existence of a fixed point of the Poincaré map associated to (1) in \(\Omega ...
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Solutions and positive solutions for superlinear Robin problems [PDF]
Journal of Mathematical Physics, 2019 We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.
N. S. Papageorgiou, C. Vetro, F. Vetro
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Boundary Value Problems, 2017 In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator.
Xinan Hao +3 more
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On the positivity of solutions of systems of stochastic PDEs [PDF]
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2012 AbstractWe study the positivity of solutions of a class of semi‐linear parabolic systems of stochastic partial differential equations by considering random approximations. For the family of random approximations we derive explicit necessary and sufficient conditions such that the solutions preserve positivity.
Messoud Efendiev +3 more
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Positive solutions of a renewal equation [PDF]
Annales Polonici Mathematici, 1992 Take the scalar integral equation \(x(t)=\int_ R h(t-s)f(s,x(s))ds\), \(t\in R\), and assume that \(h\geq 0\), \(h\in L^ 1(R)\), and that there exist positive constants \(M\), \(K\), \(\varepsilon\) such that \(0\leq f(t,x)\leq M\); \(t\in R\), \(x\in [0,\infty)\); \(f(t,x)\geq Kx\), \(t\in R\), \(x\in[0,\varepsilon)\), \(K\int_ R h(s)ds>1\).
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Positive solutions of positive linear systems
Linear Algebra and its Applications, 1985 The Volterra-Lotka equations \(dx_ i/dt=x_ i(b_ i-\Sigma a_{ij}x_ j),\) \(b_ i>0\), \(a_{ii}>0\), \(a_{ij}\geq 0\) correspond to an ecosystem with interspecies and intraspecies competition. A steady state solution \(X^*\) exists if \(b_ i-\Sigma a_{ij}X^*_ j=0\).
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