共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations −△u+a(x)u=g(x,u) in a bounded smooth domain of RN(N≥3) with the Dirichlet boundary value, where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign-changing. Recent results in the literature are generalized and significantly improved. 相似文献
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This paper deals with a generalization of the p-Laplacian type boundary value problem
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In this paper, we study the following quasilinear Schrödinger equations of the form where , , . Some existence results for positive solutions, negative solutions and sequence of high energy solutions are obtained via a perturbation method. 相似文献
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Radu Precup 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(2):834-851
We obtain critical point variants of the compression fixed point theorem in cones of Krasnoselskii. Critical points are localized in a set defined by means of two norms. In applications to semilinear elliptic boundary value problems this makes possible the use of local Moser-Harnack inequalities for the estimations from below. Multiple solutions are found for problems with oscillating nonlinearity. 相似文献
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In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|p−1u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k. 相似文献
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We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary, λ is a positive real number, and the continuous functions p
1, p
2, and q satisfy 1 < p
2(x) < q(x) < p
1(x) < N and for any . The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any is an eigenvalue, while any is not an eigenvalue of the above problem. 相似文献
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The existence of two nontrivial solutions for a class
of fully nonlinear problems at critical growth
with perturbations of lower order is proved. The first solution
is obtained via a local minimization argument while the second solution
follows by a non-smooth mountain pass theorem. 相似文献
11.
Using a recent result of Ricceri [10] we prove a multiplicity result for a class of quasilinear eigenvalue problems with nonlinear
boundary conditions on an unbounded domain. Our paper completes previous results obtained by Carstea and Rădulescu [4], Chabrowski
[1], [2], Kandilakis and Lyberopoulos [6] and Pflüger [7].
Received: 17 April 2007 相似文献
12.
Yajing Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):55-67
In this paper we study the critical growth biharmonic problem with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the biharmonic problem. 相似文献
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We consider nonlinear elliptic equations of p -Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted Lq estimates with q∈(p,∞) for the gradient of weak solutions. 相似文献
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Patrick J. Rabier 《Archiv der Mathematik》2007,88(2):143-152
We prove the existence of bounded Palais-Smale sequences for abstract functionals with a mountain pass geometry under hypotheses
weaker than those commonly used in the literature. This is obtained via a generalization of a generic result of Jeanjean,
combined with a rescaling argument. Applications to the existence of nontrivial solutions to semilinear elliptic problems
are given.
Received: 17 November 2005 相似文献
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Following Bernicot (2012) [7], we introduce a notion of paraproducts associated to a semigroup. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-Laplacian structure. Our main result is a paralinearization theorem in a non-Euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs. 相似文献
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In this paper, we find new conditions to ensure the existence of infinitely many homoclinic type solutions for the Schrödinger equation
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We study the structure of the set of solutions of a nonlinear equation involving nonhomogeneous operators:
19.
New variational principles based on the concept of anti-selfdual (ASD) Lagrangians were recently introduced in “AIHP-Analyse
non linéaire, 2006”. We continue here the program of using such Lagrangians to provide variational formulations and resolutions
to various basic equations and evolutions which do not normally fit in the Euler-Lagrange framework. In particular, we consider
stationary boundary value problems of the form as well ass dissipative initial value evolutions of the form where is a convex potential on an infinite dimensional space, A is a linear operator and is any scalar. The framework developed in the above mentioned paper reformulates these problems as and respectively, where is an “ASD” vector field derived from a suitable Lagrangian L. In this paper, we extend the domain of application of this approach by establishing existence and regularity results under
much less restrictive boundedness conditions on the anti-selfdual Lagrangian L so as to cover equations involving unbounded operators. Our main applications deal with various nonlinear boundary value
problems and parabolic initial value equations governed by transport operators with or without a diffusion term.
Nassif Ghoussoub research was partially supported by a grant from the Natural Sciences and Engineering Research Council of
Canada. The author gratefully acknowledges the hospitality and support of the Centre de Recherches Mathématiques in Montréal
where this work was initiated.
Leo Tzou’s research was partially supported by a doctoral postgraduate scholarship from the Natural Science and Engineering
Research Council of Canada. 相似文献
20.
Behzad Djafari Rouhani Hadi Khatibzadeh 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e147
By using previous results of Djafari Rouhani [B. Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale university, 1981, part I, pp. 1-76; B. Djafari Rouhani, Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces, J. Math. Anal. Appl. 147 (1990) 465-476; B. Djafari Rouhani, Asymptotic behaviour of almost nonexpansive sequences in a Hilbert space, J. Math. Anal. Appl. 151 (1990) 226-235] for dissipative systems, we study the asymptotic behavior of solutions to the following system of second-order nonhomogeneous evolution equations: