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Existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight
J. Tyagi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2882-2889
We prove the existence of nonnegative solutions to the system
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The existence of multiple positive solutions of systems of singular Hammerstein integral equations is studied, where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear Hammerstein integral operators. Such systems contain some mathematical models arising in science and engineering. Applications are given to the existence of multiple positive radial solutions of systems of semilinear singular elliptic equations in annuli on which, to the best of our knowledge, there has been little study. 相似文献
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Yasuhito Miyamoto 《Journal of Differential Equations》2018,264(4):2684-2707
We study radial solutions of the semilinear elliptic equation under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., and . 相似文献
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Hiroyuki Chihara 《Journal of Differential Equations》2009,246(2):681-723
We discuss gain of analyticity phenomenon of solutions to the initial value problem for semilinear Schrödinger equations with gauge invariant nonlinearity. We prove that if the initial data decays exponentially, then the solution becomes real-analytic in the space variable and a Gevrey function of order 2 in the time variable except in the initial plane. Our proof is based on the energy estimates developed in our previous work and on fine summation formulae concerned with a matrix norm. 相似文献
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Kai-Seng Chou Shi-Zhong Du Gao-Feng Zheng 《Calculus of Variations and Partial Differential Equations》2007,30(2):251-275
The global, weak solutions for the semilinear problem (1) introduced in Ni-Sacks-Tavantzis (J. Differ. Eq. 54, 97–120 (1984)) are studied. Estimates on the Hausdorff dimension of their singular sets are found. As an application, it
is shown that these solutions must blow up in finite time and become regular eventually when the nonlinearity is supercritical
and the domain is convex. 相似文献
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Layered solutions for a semilinear elliptic system in a ball 总被引:1,自引:0,他引:1
We consider the following system of Schrödinger-Poisson equations in the unit ball B1 of R3:
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We study the Hölder regularity of weak solutions to the evolutionary p -Laplacian system with critical growth on the gradient. We establish a natural criterion for proving that a small solution and its gradient are locally Hölder continuous almost everywhere. Actually our regularity result recovers the classical result in the case p=2 [16] and can be applied to study the regularity of the heat flow for m-dimensional H-systems as well as the m-harmonic flow. 相似文献
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In this paper we study a simple non-local semilinear parabolic equation in a bounded domain with Neumann boundary conditions. We obtain a global existence result for initial data whose L∞-norm is less than a constant depending explicitly on the geometry of the domain. A natural energy is associated to the equation and we establish a relationship between the finite-time blow up of solutions and the negativity of their energy. The proof of this result is based on a Gamma-convergence technique. 相似文献
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In this paper we obtain a new global gradient estimates in weighted Lorentz spaces for weak solutions of p(x)-Laplacian type equation with small BMO coefficients in a δ-Reifenberg flat domain. The modified Vitali covering lemma, the maximal function technique and the appropriate localization method are the main analytical tools. Our results improve the known results for such equations. 相似文献
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We construct positive solutions of the semilinear elliptic problem with Dirichet boundary conditions, in a bounded smooth domain Ω⊂RN(N?4), when the exponent p is supercritical and close enough to and the parameter λ∈R is small enough. As , the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green's function. Our result extends the result of Del Pino et al. (J. Differential Equations 193(2) (2003) 280) when Ω is a ball and the solutions are radially symmetric. 相似文献
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Blow-up for semilinear parabolic equations with nonlinear memory 总被引:4,自引:0,他引:4
In this paper, we consider the semilinear parabolic
equation
with homogeneous Dirichlet boundary conditions, where
p, q are
nonnegative constants. The blowup criteria and the blowup rate
are obtained. 相似文献
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Eurica Henriques 《Journal of Differential Equations》2008,244(10):2578-2601
We extend to the singular case the results of [E. Henriques, J.M. Urbano, Intrinsic scaling for PDEs with an exponential nonlinearity, Indiana Univ. Math. J. 55 (5) (2006) 1701-1721] concerning the regularity of weak solutions of the porous medium equation with variable exponent. The method of intrinsic scaling is used to show that local weak solutions are locally continuous. 相似文献
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J. Chabrowski 《Journal of Fixed Point Theory and Applications》2007,2(2):333-352
We investigate the solvability of the Neumann problem involving the critical Sobolev exponent, the Hardy potential and a nonlinear
term of lower order. Lower order terms are allowed to interfere with the spectrum of the operator subject to the Neumann boundary conditions. Solutions are obtained via a min-max procedure based on the variational mountain-pass
principle and topological linking.
相似文献
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Noriko Mizoguchi 《Journal of Differential Equations》2006,227(2):652-669
We consider a Cauchy problem for a semilinear heat equation
(P) 相似文献