1,721,003 research outputs found
On the solutions of quasilinear elliptic equations with a polynomial-type reaction term
No full textWe study existence and boundedness of solutions for the
quasilinear elliptic equation −Δ_m u = λ(1+u)^p in a bounded domain Ω
with homogeneous Dirichlet boundary conditions. The assumptions on
both the parameters λ and p are fundamental. Strange critical exponents
appear when boundedness of solutions is concerned. In our proofs we
use techniques from calculus of variations, from critical-point theory,
and from the theory of ordinary differential equations
Least energy solutions for critical growth equations with a lower order perturbation
No full textWe study existence and nonexistence of least energy solutions
of a quasilinear critical growth equation with degenerate m-Laplace
operator in a bounded domain in R^n with n > m > 1. Existence and
nonexistence of solutions of this problem depend on a lower order perturbation
and on the space dimension n. Our proofs are obtained with
critical point theory and the lack of compactness, due to critical growth
condition, is overcome by constructing minimax levels in a suitable compactness
range
Existence and multiplicity results for semilinear elliptic equations with measures and jumping nonlinearities
No full textWe study existence and multiplicity results for semilinear elliptic equations of the type -\Delta u = g(x, u) - te_1 + \mu with homogeneous Dirichlet boundary conditions. Here g(x, u) is a jumping nonlinearity, \mu is a Radon measure, t is a positive constant and e_1 > 0 is the first eigenfunction of -\Delta. Existence results strictly depend on the asymptotic behavior of g(x, u) as u -> \pm \infty. Depending on this asymptotic behavior, we prove existence of two and three solutions for t > 0 large enough. In order to find solutions of the equation, we introduce a suitable action functional I_t by mean of an appropriate iterative scheme. Then we apply to I_t standard results from the critical point theory and we prove existence of critical points for this functional
A partially hinged rectangular plate as a model for suspension bridges
Full text linkA plate model describing the statics and dynamics of a suspension bridge is suggested. A partially hinged plate subject to nonlinear restoring hangers is considered. The whole theory from linear problems, through nonlinear stationary equations, ending with the full hyperbolic evolution equation is studied. This paper aims to be the starting point for more refined models
Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations
No full textA monotonicity approach to the study of the asymptotic behaviour near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces
Existence and Multiplicity Results for Semilinear Elliptic Equations with Measure Data and Jumping Nonlinearities
No full textWe study existence and multiplicity results for semilinear elliptic equations of the type
−∆u = g(x, u) − te_1 + μ
with homogeneous Dirichlet boundary conditions. Here g(x, u) is a jumping nonlinearity, μ is a Radon measure, t is a positive constant and e_1 > 0 is the first eigenfunction of −∆. Existence results strictly depend on the asymptotic behavior of g(x, u) as u → ±∞. Depending on this asymptotic behavior, we prove existence of two and three solutions for t > 0 large enough. In order to find solutions of the equation, we introduce a suitable action functional I_t by means of an appropriate iterative scheme. Then we apply to It standard results from the critical point theory and we prove existence of critical points for this functional
Existence and Multiplicity Results for Semilinear Equations with Measure Data
No full textIn this paper, we study existence and nonexistence of solutions for the Dirichlet problem
associated with the equation −∆u = g(x, u) + μ where μ is a Radon measure. Existence and
nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions
are assumed on it. Our proofs are obtained by standard arguments from critical theory and in order
to find solutions of the equation, suitable functionals are introduced by mean of approximation
arguments and iterative schemes
On the behavior at collisions of solutions to Schrodinger equations with many-particle and cylindrical potentials
No full textThe asymptotic behavior of solutions to Schr ̈odinger equations
with singular homogeneous potentials is investigated. Through an Almgren
type monotonicity formula and separation of variables, we describe the exact
asymptotics near the singularity of solutions to at most critical semilinear elliptic
equations with cylindrical and quantum multi-body singular potentials.
Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate
are derived
A Note on Local Asymptotics of Solutions to Singular Elliptic Equations via Monotonicity Methods
No full textThis paper concerns the asymptotic behavior of solutions and their
gradients to linear and nonlinear elliptic equations with singular coefficients of
fuchsian type
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